Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we discuss the possibility of constructing a quantum clock, which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.

Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.

During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.

Recent advances in the theory of quantum gravity show that the Ricci flow serves as the time evolution operator for the vacuum energy density and that in the presence of baryonic matter, the Ricci flow is analogous to the heat equation in the presence of a heat sink. Here we show using the equations of quantum gravity, that quantum information can be modelled as a thermal fluid consisting of a superposition of weakly excited eigenstates of a quantum field and that each eigenstate vector has an associated eigenstate potential well. The depth of the potential well depends on the amplitude of the eigenstate vector. Measurement is then considered as a selection by tuning process which only allows an eigenstate resonating with the detector to be detected. During the detection process, the resonating eigenstate vector increases in amplitude, deepening its potential well such that the other weakly excited states rapidly drain their small excitation energies into it via the principle of minimum action. This draining process is the act of collapsing the wave function to a specific state. Also, the presence of the eigenstate potential wells is what cancels out the infinities from high energy interactions.

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to currently not provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed `quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

In this paper, the connections between quantum non-locality and permutation symmetries are explored. This includes two types of symmetries: permutation across a superposition and permutation of qubits in a quantum system. An algorithm is proposed for nding the separability class of a quantum state using a method based on factorizing an arbitrary multipartite state into possible partitions, cyclically permuting qubits of the vectors in a superposition to check which separability class it falls into and thereafter using a reduced density-matrix analysis of the system is proposed. For the case of mixed quantum states, conditions for separability are found in terms of the partial transposition of the density matrices of the quantum system. One of these conditions turns out to be the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separability is also proposed. The concept of permutation of qubits is shown to be useful in dening a new entanglement measure in the `engle'.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Cs2NaInCl6 double perovskites, which have excellent photoelectric conversion properties and are non-toxic and lead-free, have recently attracted much attention. In particular, double perovskite quantum dots (QDs) are considered to be a promising material for optoelectronic device applications. Ligands such as oleic acid (OA) and oleylamine (OAm) are essential for the synthesis of perovskite QDs, but their roles on double perovskite QDs are not yet clear. In this study, we have investigated the binding of OA and OAm to Cs2NaInCl6 QDs through FTIR and NMR and their effects on the surface defect reduction and stability improvement for Cs2NaInCl6 QDs. We found that only OAm was bound to the QD surfaces while OA was not. The OAm has a great effect on photoluminescence quantum yield (PLQY) improvement by passivate the QD surface defects. The stability of the QDs was also investigated, and it was shown that OA played a significant role in the stability of the QDs. Our findings provide critical insights into the roles of the ligands for photophysical properties and stability of lead-free double perovskite QDs.

This paper gives solutions to puzzles of double Wheeler’s delayed choice experiments, a photon’s passing two paths simultaneously and wave collapse velocity measure, and shows new quantum control, new quantum oscillation and new controlling photon oscillator (that can be arranged in quantum computer and quantum network as their classical correspondences) in experiments. Furthermore, this paper obtains the measured attractive state and the new useful key technology of altering state’s evolving paths for quantum systems. We discover the reason and the technological way for the present changes the past, further show their feasible experiments of new quantum control, new quantum oscillation and new quantum oscillator. Finally, this paper achieves the collapse response time t of wave, further concretely deduces the measured collapse velocity of quantum system. In the past, the collapse velocity cannot be objectively deduced and experimentally measured.

A variant of the von Neumann-Wigner Interpretation is proposed. It does not make use of the familiar language of wave functionsand observers. Instead it pictures the state of the physical world as a vector in a Fock space and, therefore not, literally, a functionof any spacetime coordinates. And, rather than segregating consciousness into individual points of view (each carrying with it asense of its proper time), this model proposes only unitary states of consciousness, Q(t), where t represents a fiducial time withrespect to which both the state of the physical world and the state of consciousness evolve. States in our world's Fock space areclassified as either 'admissible' (meaning they correspond to definite states of consciousness) or 'inadmissible' (meaning they donot). The evolution of the state vector of the world is such as to always keep it restricted to 'admissible' states. Consciousness istreated very much like what Chalmers calls an "M-Property." But we try to show that problems with the quantum Zeno effect do not arise from this model.

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

The double nature, wave and corpuscular, of the material particles is usually considered incomprehensible as it cannot be represented visually. It is proposed to the student, in the introductory courses, as a fact justified by quantum interference experiments of which, however, no further analysis is possible. In this note we propose a description of the wave function in terms of a simple electrical analogy, which reproduces at least some of its essential properties. The aim we propose is to provide a cognitive representation of an analogical type: starting from a classical context (electrical circuits) and introducing in an appropriate way the notions of "wave" and "particle", we show how typically quantum properties such as delocalization and entanglement emerge in a natural, understandable and intuitive way.

Quantum mechanics is often described as irreducibly non-local. A tacit element of this picture is the assumption that one and the same sub-ensemble of quanta is post-selected in every measurement combination of a Bell test. Yet, this expectation was recently shown to be formally inconsistent with quantum theory (Cetto et al., 2020) and even to be experimentally falsifiable (Mardari 2021). The need to make sense of this development motivated a rigorous conceptual analysis of quantum non-locality, especially as it relates to the basic principles of quantum mechanics. The simple conclusion is that quantum theory and quantum non-locality are fundamentally incompatible. This is not a loophole around the predictions of quantum mechanics, but rather an insight into the essential conditions that make them accurate.

Classical mechanics describes the laws of motion in the macroscopic material world, while quantum mechanics describes the laws of motion in the microscopic material world that classical mechanics cannot explain, and achieves a highly accurate mathematical representation of the laws of microscopic physical motion. But even with such a successful theory, there is confusion about the probability wave. Therefore, this paper attempts to improve the physical definition of the conceptual basis of quantum mechanics, thus solving the confusion of quantum mechanical probability waves, and finally surprisingly discovered another feasible interpretation of the principle of cosmic redshift and the invariance of the speed of light.

In the past 100 years, quantum theory has achieved remarkable achievements and formed a relatively mature system, but at the same time there are still some incomplete places. For example: What is the origin of quantum? What is the origin of quantum entanglement? What is the origin of quantum mechanical wave-particle duality? This is still a problem that the existing quantum theory has not solved. Therefore, this paper attempts to seek a classic interpretation of quantum mechanics to make up for the shortcomings of existing quantum theory. In the latest research, this paper finds a classic interpretation of blackbody radiation, which can explain the discontinuity of light energy from the perspective of classical mechanics. Based on this discovery, this paper successfully explains the origin of quantum, quantum entanglement and wave-particle duality, and eliminates the confusion of quantum mechanical probability waves.

We show that the accelerating expansion phase of the universe can emerge from the group field theory formalism, a candidate theory of quantum gravity. The cosmological evolution can be extracted from condensate states using mean field approximation, in a form of modified FLRW equations. By introducing an effective equation of state w, we can reveal the relevant features of the evolution, and show that with proper choice of parameters, w will approach to −1, corresponds to the behaviour of cosmological constant, results in a late time acceleration and leads to de Sitter spacetime asymptotically.

The design and operation of quantum networks are both decisive in the current push towards a global quantum internet. Although space-enabled quantum connectivity has already been identified as a beneficial candidate for long-range quantum channels for over two decades, the architecture of a hybrid space-ground network is still a work in progress. Here, we propose an analysis of such a network based on a best-path approach, where either fiber- or satellite-based elementary links can be concatenated to form a repeater chain. The network consisting of quantum information processing nodes, equipped with both ground and space connections, is mapped into a graph structure, where edge weights represent the achievable secret key rates, chosen as the figure of merit for the network analysis. A weight minimization algorithm allows identifying the best path dynamically, i.e., as the weather conditions, stray light radiance, and satellite orbital position changes. From the results we conclude that satellite links will play a significant role on the future large-scale quantum internet, and both a constellation of satellites and significant advances in filtering technology are required to fulfill continuous coverage.

In this paper, I propose new models of quantum information processing using the exchange interaction in physical systems. The partial SWAP operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence-free subspaces. Given the non-commutativity of these operators (for adjacent operators operating on a common qubit), a number of quantum states and entanglement patters can be obtained. This zoo of states can be classified, due to the parity constraints and permutation symmetry of the states, into invariant subspaces that are used for the definition of some of the applications in this paper.

Quantum Computation, in the gate array version, uses logical gates adopting convenient forms for computational algorithms based on those of classical computation. There, two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite, their design depends on specific quantum systems and physical interactions involved, exacerbating the dynamics analysis. Predictable and controllable manipulation should be addressed to control the quantum states, but resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in SU(2^2d) for 2d-partite two-level systems into 2^2d-1 SU(2) quantum subsystems. Decomposition lets to set control procedures, to generate large entangled states and to design specialized dedicated quantum gates. There, easy and traditional operations proposed by quantum computation are recovered for more complex and large systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the generalized Bell states basis. It could be understood as a momentary splitting of the 2d information channels into 2^2d-1 pairs of 2 level quantum information subsystems and a settlement of the quantum information manipulation free of the imposed restrictions by the underlying physical system.

The potential of quantum computing for scientific and industrial breakthroughs is immense, however, we are still in the Noisy Intermediate-Scale Quantum (NISQ) era, where the currently available quantum devices contain small numbers of qubits, are very sensitive to environmental conditions and prone to quantum decoherence. Even so, existing NISQ computers have already been shown to outperform conventional computers on specific problems and the key question is how to make use of today’s NISQ devices to achieve quantum advantage in the field of computational science and engineering (CSE). In this direction, this work proposes a hybrid computing formulation by combining quantum computing with machine learning for accelerating the solution of parameterized linear systems in NISQ devices. In particular, it focuses on the Variational Quantum Linear Solver (VQLS), which is a hybrid quantum- classical algorithm for solving linear systems of equations. VQLS employs a short-depth quantum circuit to efficiently evaluate a cost function related to the system solution. The algorithm’s circuit consists of a quantum gate sequence (unitary operators) that involves a set of tunable parameters. Then, well-established classical optimizers are utilized to tune the parameters of the sequence in order to minimize the cost function, which is equivalent to finding the system solution at an acceptable level of accuracy. In this work, it is demonstrated that machine learning tools such as feed-forward neural networks and nearest-neighbor interpolation techniques can be successfully employed to accelerate the convergence of the VQLS algorithm towards the optimal values for the circuit parameters when applied to parameterized linear systems that need to be solved for multiple parameter instances.

A simplified version of the quantum teleportation protocol is presented in here. Its experimental confirmation will have deep implications for a better understanding of Quantum Entanglement with a particular projection on Quantum Communications.

We argue that a very large class of quantum pure states of isolated macroscopic bodies have sharply peaked energy distributions, with their width relative to the average scaling between $\sim N^{-1}$ and $\sim N^{-1/2}$, with $N \gg 1$, the number of atoms conforming the body. Those states are dense superpositions of energy eigenstates within arbitrary finite or infinite energy intervals that decay sufficiently fast. The sharpness of the energy distribution implies that closed systems in those states are {\it microcanonical} in the sense that only energy eigenstates very near to the mean energy contribute to their thermodynamic evolution. Since thermodynamics accurately describes processes of macroscopic bodies and requires that closed systems have constant energy, our claim is that these pure states are typical of macroscopic systems. The main assumption beneath the energy sharpness is that the isolated body can reach thermal equilibrium if left unaltered. We argue that such a self-sharpness of the energy in macroscopic bodies indicates that the First Law of Thermodynamics is statistical in character.

In magneto-photoluminescence (magneto-PL) spectra of quasi-two dimensional islands (quantum dots) having seven electrons and Wigner-Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts and jumps of the energy of the emission components for filling factors >1 (B<10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock-Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, Majorana anyon origin of the states having even , i.e., composite fermions, which provide new opportunities for topological quantum computing.

The rapid development of quantum computing devices promises powerful machines with capabilities that solve a wide range of problems that traditional computers cannot. Therefore, quantum computers generate new threats at unprecedented speed and scale and specifically pose an enormous threat to encryption. Lattice-based cryptography is considered to be the rival to a quantum computer attack and the future of post-quantum cryptography. So, cryptographic protocols based on lattices have a variety of benefits, like security, efficiency, lower energy consumption, and speed. In this work, we study the most well-known lattice-based cryptosystems while a systematic evaluation and comparison is presented also, and focuses on their strengths and weaknesses.

We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of quantum evolution, which give similar results explicitly. The relevance of these approaches to building a quantum theory of gravity is discussed.

In this note, we demonstrate the quantum no-hiding theorem of Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)] using the IBM 5Q quantum processor. We also analyze the circuit using the ZX calculus of Coecke and Duncan [New J Phys. 13(4), 043016 (2011)], which provides a pictorial/category-theoretic demonstration of the no-hiding theorem.

In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the Variational Quantum Classifier (VQC) and the Quantum Kernel Estimator (QKE). We evaluate the performance of these classifiers on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, we developed a data set based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results.\\ Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers like XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes.\\ Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field.\\ To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.

Having access to a unique quantum circuit that one wants to protect against use by others is a very likely scenario. However currently users rely on classical computer security schemes, which have known shortcomings. In this chapter we introduce a novel protection scheme along with a survey of other known methods to protect quantum information. In particular we review physically unclonable functions (PUFs), obfuscation, and introduce quantum logic locking.

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory.

A physical scrutiny of experimental results published in Physical Review Letters (December 2015, M. Giustina, et al., Phys. Rev. Lett. 115, 250401, and L. K. Shalm et al., Phys. Rev. Lett. 115, 250402) is undertaken. These articles reported that measured outcomes were fitted with quantum states possessing a dominant component of non-entangled photons, thereby contradicting their own claim of quantum nonlocality. With probabilities of photon detections lower than 0.1 %, the alleged quantum nonlocality cannot be classified as a resource for developing quantum computing devices, despite recent publicity. Experimental evidence of a feasible process for quantum-strong correlations has been identified (M. Iannuzzi, et al., Phys. Lett. A, 384 (9), 126200, 2020) in terms of correlations between independent and multi-photon states evaluated as Stokes vectors on the Poincaré sphere. As single-photon sources are not needed, the design and implementation of quantum computing operations will be significantly streamlined.

This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary "particles''. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

Quantum entanglement is a fascinating topic with both theoretical and technological impacts. Yet, even in the simplest scenarios, there are still various open questions involving pure state and mixed state entanglement. Here we present the simplest entangled mixed states. We consider both qubits (quantum bits) and qudits (quantum digits). We first provide our simplest yet most important result for rank-2 bi-partite states, and we then generalize our results to go beyond rank-2 and to go beyond bi-partite states.

Tremendous progress has been witnessed in artificial intelligence within the domain of neural network backed deep learning systems and its applications. As we approach the post Moore’s Law era, the limit of semiconductor fabrication technology along with a rapid increase in data generation rates have lead to an impending growing challenge of tackling newer and more modern machine learning problems. In parallel, quantum computing has exhibited rapid development in recent years. Due to the potential of a quantum speedup, quantum based learning applications have become an area of significant interest, in hopes that we can leverage quantum systems to solve classical problems. In this work, we propose a quantum deep learning architecture; we demonstrate our quantum neural network architecture on tasks ranging from binary and multi-class classification to generative modelling. Powered by a modified quantum differentiation function along with a hybrid quantum-classic design, our architecture encodes the data with a reduced number of qubits and generates a quantum circuit, loading it onto a quantum platform where the model learns the optimal states iteratively. We conduct intensive experiments on both the local computing environment and IBM-Q quantum platform. The evaluation results demonstrate that our architecture is able to outperform Tensorflow-Quantum by up to 12.51% and 11.71% for a comparable classic deep neural network on the task of classification trained with the same network settings. Furthermore, our GAN architecture runs the discriminator and the generator purely on quantum hardware and utilizes the swap test on qubits to calculate the values of loss functions. In comparing our quantum GAN, we note our architecture is able to achieve similar performance with 98.5% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms other quantum based GANs in the literature for up to 125.0% in terms of similarity between generated distributions and original data sets.

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum $ P(k) $ and the CMB temperature angular power spectrum $ C_l $’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients $ C_l $, which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

Atomtronics is a relatively new subfield of atomic physics that aims to realize the device behavior of electronic components in ultracold atom-optical systems. The fact that these systems are coherent makes them particularly interesting since, in addition to current, one can impart quantum states onto the current carriers themselves or perhaps perform quantum computational operations on them. After reviewing the fundamental ideas of this subfield, we report on the theoretical and experimental progress made towards developing externally-driven and closed loop devices. The functionality and potential applications for these atom analogs to electronic and spintronic systems is also discussed.

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured at the same time. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

Classic game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the Prisoner's Dilemma (PD), have attracted a lot of attention. Similarly, state machines and specifically finite automata have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine some well-known game conditional strategies that have been studied within the framework of the repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with probability 1, achieving some interesting results. We also study the quantum version of PD under the Eisert-Wilkens-Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

The paper discusses the design and modeling of a simple and illustrative hardware kit for teaching the basics of quantum cryptography to engineering students. The novel solution differs from those already on the market in that it is focused on familiarising trainees with the physical principles of quantum key distribution, as well as with the basics of mathematical formalism in quantum mechanics. This is achieved by using a minimally sufficient set of optical elements with a simple mathematical description in the Jones formalism. This composition of the kit is targeted mostly at engineering students and does not require advanced training in physics as a prerequisite. The configurable architecture of the hardware educational kit contributes to the deeper involvement of students. By independently changing the modular configuration of the system, students can conduct experiments that were not directly provided by the developers. For instance, students can assess the impact of choosing the basic settings of phase retarders on the course of a man-in-the-middle attack. The proposed amount of mathematical and informational support, as well as ready-made formal models, is sufficient to reasonably put forward hypotheses for experimental verification and interpret the obtained empirical data. At this moment, the hardware kit is being replicated, distributed and successfully applied at universities and companies in the communications industry. The accumulated experience of educational use testifies to the high efficiency of the kit as a tool for basic QKD training for people without prior knowledge of quantum mechanics. A discrete event model simulating the operation of the hardware kit is implemented in the non-commercial modeling software CPN Tools and is openly distributed.

We present detailed models at the hydrodynamics and decoherence phenomena observed in ideal quantum gases. The model is expressed in terms of a quantum field theory, where the action involves both hydrodynamic and decoherence terms. The density-current relation is derived, and the current Green function is introduced. The effective action for two fields is presented, and the physical field is defined in terms of the bare action. Identities such as CTP symmetry, transposition, and the Ward identity are discussed. The Green function and its inverse for different components are also explored. These notes provide a comprehensive understanding of the theoretical framework for studying the hydrodynamics and decoherence of ideal quantum gases.

We have shown that according to the predictions of the standard quantum theory, signaling is possible using a postponed compensation Hong-Ou-Mandel interferometer, although it violates Lorentz invariance. We argue that new physics is required to deal with such a paradox. Either quantum principles or relativity needs reassessment. We propose an experiment that can decide whether relativity rules over quantum or vice versa.

Black hole collision produce gravitational radiation which is generally thought in a quantum limit to be gravitons. The stretched horizon of a black hole contains quantum information, or a form of quantum hair, which in a coalescence of black holes participates in the generation of gravitons. This may be facilitated with a Bohr-like approach to black hole (BH) quantum physics with quasi-normal mode (QNM) approach to BH quantum mechanics. Quantum gravity and quantum hair on event horizons is excited to higher energy in BH coalescence. The near horizon condition for two BHs right before collision is a deformed AdS spacetime. These excited states of BH quantum hair then relax with the production of gravitons. This is then argued to define RT entropy given by quantum hair on the horizons. These qubits of information from a BH coalescence should then appear in gravitational wave (GW) data. This is a form of the standard AdS/CF T correspondence and the Ryu-Takayanagi (RT) formula [1]. The foundations of physics is proposed to be quantum information and a duality between spacetime observables and quantum fields.

Patterning, stability, and dispersion of the semiconductor quantum dots (scQDs) are the three issues strictly interconnected for successful device manufacturing. Recently several authors adopted direct optical patterning (DOP) as a step forward in photolithography to position the scQDs in a selected area. However, the chemistry behind the stability, dispersion, and patterning has to be carefully integrated to obtain a functional and therefore, commercial device. In this review are described different chemical strategies suitable to stabilize the scQDs both at a single level and as an ensemble with a special focus on the ones compatible with direct optical patterning (DOP). With the same purpose, the scQDs dispersion in a matrix was described in terms of the scQDs surface ligands interactions with the matrix itself. The chemical processes behind the DOP are illustrated and discussed for five different approaches that consider together stability, dispersion, and the patterning itself of the scQDs.

Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) is a two-photon protocol devised to eliminate eavesdropping attacks that interrogate or control the detector in realized quantum key distribution systems. In MDI-QKD, the measurements are carried out by an untrusted third party, and the measurement results are announced openly. Knowledge or control of the measurement results gives the third party no information about the secret key. Error-free implementation of the MDI-QKD protocol requires the crypto-communicating parties, Alice and Bob, to independently prepare and transmit single photons that are physically indistinguishable, with the possible exception of their polarization states. In this paper, we apply the formalism of quantum optics and Monte Carlo simulations to quantify the impact of small errors in wavelength, bandwidth, polarization and timing between Alice's photons and Bob's photons on the MDI-QKD quantum bit error rate (QBER). Using published single-photon source characteristics from two-photon interference experiments as a test case, our simulations predict that the finite tolerances of these sources contribute (4.04+/-20/N_sifted) to the QBER in an MDI-QKD implementation generating an N_sifted-bit sifted key.

Chemistry has been viewed as one of the most fruitful near-term applications to science of quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Much less effort has been placed on how one finishes these calculations by using the results from the quantum computer (on the active region of the molecule) and embeds them back into the remainder of the molecule in order to determine the properties of the entire molecule. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with classical algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

The ability to control the flow of quantum information deterministically is useful for scaling up quantum computation. In this paper, we demonstrate a controllable quantum switchboard which directs the teleportation protocol to one of two targets, fully dependent on the sender’s choice. The quantum switchboard additionally acts as a optimal quantum cloning machine. We also provide a physical implementation of the proposal using a coupled-cavity array. The proposed switchboard can be utilized for the efficient routing of quantum information in a large quantum network.

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. In this paper, generation, characterisation and application of a genuine genuinely entangled seven-qubit resource state is studied. Theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation as well as three schemes for undertaking tripartite quantum state sharing are presented.

We study the performance of a classical and quantum magnetic Otto cycle with a quantum dot as a working substance using the Fock-Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, we found in the classical approach an oscillating behavior in the total work that is not perceptible under the quantum formulation. Also, we compare the work and efficiency of this system for different regions of the Entropy, $S(T,B)$, diagram where we found that the quantum version of this engine always shows a reduced performance in comparison to his classical counterpart.

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

Any photon, regardless of its origin, carries the same optical field profile. This feature and the quantum Rayleigh emissions generate temporally discrete groups of several photons in a resonant cavity incorporating one single quantum dot. A periodic stream of single photons is distorted by high-finesse optical cavities and the quantum Rayleigh spontaneous emission in a beam splitter. Groups of photons emerge from interferometric filters because of multiple internal reflections.

Starting with unitary quantum dynamics, we investigate how to add quantum measurements. Quantum measurements have four essential components: the furcation, the witness production, an alignment projection, and the actual choice decision. The first two components still lie in the domain of unitary quantum dynamics. The decoherence concept explains the third contribution. It can be based on the requirement that witnesses reaching the end of time on the wave function side and the conjugate one have to be identical. In this way, it also stays within the quantum dynamics domain. The surjection hypothesis explains the actual choice decision. It is based on a two boundary interpretation applied to the complete quantum universe. It offers a simple way to reduce these seemingly random projections to purely deterministic unitary quantum dynamics, eliminating the measurement problem.

Two opposed p–n diodes are connected with another junction that causes cancellation of the electric field in the depletion layer of each diode by the field of the other diode. This derived quantum diode is called the A system. Another dual diode, constructed by the same process but with the p- and n-types positioned as duality, called the B system. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts a momentum (i.e., a wave number) to the carriers in the absence of any internal voltage. Thus, a superconducting bias current density appears without the need for cooling. The reappearances of electron–hole pairs on the junction surfaces are assumed to be described by entire wavefunctions normalized by the band gap. Based on the bias superconducting current, NOT and NAND gates were constructed from the quantum diode systems. Numerical calculations revealed that the constant phases of the entire wavefunctions of the p-and n-types converged. Accordingly, it was clarified that Bose–Einstein condensation and the Meissner effect (described by the London equation) occurred in the quantum diode systems. Moreover, the systems exhibited rectification characteristics and a switching speed of the order of 10^-14 s. Combining this switching property with the large bias superconducting current (of the order of several V), we developed NOT and NAND gates with direct quantum correlations among many qubits, which are unaffected by random and thermal noises. These gates have memorization and initialization properties and are compatible with existing and accumulating programing algorithms. Moreover, when harvesting a divergent current output from these systems, the bias superconducting current and memorization property preserve the formed quantum correlations.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides a mathematical framework in which the description of a physical system in curved spacetime and its description in a flat spacetime with fields are equivalent. As demonstrated in previous publications, in curved spacetime this tensor reproduces Einstein Field Equations and in flat Minkowski spacetime, it describes physical system with fields that can be widely configured. Thanks to the obtained compliance with QM and QED, the use of the discussed tensor may significantly simplify Quantum Field Theory equations and a new interpretation of the Schrödinger equation is possible. In the article it has also been shown that the use of Alena Tensor for the electromagnetic field takes into account effects related to the particle's spin, Abraham–Lorentz effect and, in the curvilinear description, this excludes non-physical phenomena such as the black hole singularity. The article contains a method for verifying Alena Tensor within QM, proposing an explanation for the discrepancy between the Dirac and Klein-Gordon solutions. It also discusses prospects for the application of Alena Tensor in unification theories against the background of existing research directions.

The drug discovery process is a rigorous and time-consuming endeavor, typically requiring several years of extensive research and development. Although classical machine learning (ML) has proven successful in this field, its computational demands in terms of speed and resources are significant. In recent years, researchers have sought to explore the potential benefits of quantum computing (QC) in the context of ML, leading to the emergence of Quantum Machine Learning (QML) as a distinct research field. The objective of the current study is twofold: first, to present a review of the proposed QML algorithms for application in the drug discovery pipeline, and second, to compare QML algorithms with their classical and hybrid counterparts in terms of their efficiency. A query-based search of various databases took place, and five different categories of algorithms were identified in which QML was implemented. The majority of QML applications in drug discovery are primarily focused on the initial stages of the drug discovery pipeline, particularly with regard to the identification of novel drug-like molecules. Comparison results revealed that QML algorithms are strong rivals against the classical ones and a hybrid solution is the recommended approach at present.

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter Physics" we demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following canonical quantization technique. In this computation, two dynamical time scales are involved, out of them at one time scale the cosmological perturbation variable and for the other the canonically conjugate momentum is defined, which is the strict requirement to define time scale separated quantum operators for OTOC and perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism not only one can study the quantum correlation during stochastic inflation and reheating, but also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism we study the phenomena of quantum chaos by computing the expression for {\it Lyapunov spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS) bound, on Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing but not exponentially decaying behaviour, which quantifies the random correlation at out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to check the consistency with the large time limiting behaviour.

In recent years, genetic research has been developing rapidly and taking on a larger role in research and medicine. The synthesis of any particle that can be used in this research can pave the way for new developments in this field. This research aims to develop a chemical method to produce nitrogen-doped carbon quantum dots - economical and bio-sourced substances that bind to genomic DNA. Carbon quantum dots are produced by the green synthesis hydrothermal method from radish, which is abundant in nature, and economically affordable. Nitrogen is added to increase the fluorescence properties of the produced carbon quantum dots and to improve their binding to DNA. The synthesized nitrogen-doped carbon quantum dots (N-CQDs) were tested through chromosome imaging subsequently. It was shown that N-CQDs can bind to the chromosomes, and N-CQDs reflected green light better than DAPI under the FITC filter, a potential advantage of using N-CQDs over DAPI in chromosome imaging.

We propose a new binary formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. Furthermore, we present a detailed study of the constraints used and compare our model (GPS) with other frequent formulations (MTZ and native formulation). Finally, we have carried out a coherence and efficiency check of the proposed formulation by running it on a quantum annealing computer, D-Wave\_2000Q6.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

The new Post Accelerating Data and Knowledge Online Society, or ‘Padkos’ requires a new model of decision making. This introductory paper proposes a model where decision making and learning are a single symbiotic process, incorporating man and machine, as well as the AADD (ánthrōpos, apparatus, decider, doctrina) diamond model of individual and organizational decision-making and learning processes. The learning is incorporated by using a newly proposed quadruple loop learning model. This model allows for controlled changes of identity, the process of creating and the sense making of new mental models and assumption, and reflections. The model also incorporates the recently proposed model of quantum decision-making, where time collapse of the opted past and the anticipated future (explicitly including its time horizon) into the present play a key role in the process, leveraging decision-making and learning by human as well as Artificial Intelligence (AI) and Machine Learning (ML) algorithms. The paper closes with conclusions.

In this review, the author shows that ferritin has documented quantum dot material properties that have been reported in numerous independent studies and can generate coherent electron conduction bands over substantial distances, using quantum coherence. In addition, neuromelanin is a conjugated polymer, and quantum dot/conjugated polymer combinations have been reported in numerous independent studies to generate coherent electron conduction bands for solar photovoltaic applications. Both ferritin and neuromelanin are present in large quantities in the dopamine neurons of the substantia nigra pars compacta and the norepinephrine neurons of the locus coeruleus. The unique structure of subgroups of these neurons that have a large number of axon branches and synapses appears to have evolved to take advantage of these coherent electron conduction bands to coordinate conscious action. Independent clinical and laboratory studies are also reviewed that corroborate this theory of coordinated action in these neuron groups. Proposed research to validate the theory using an existing fluorescent probe material is proposed.

This short paper briefly explores the interplay between quantum mechanics and gravity, drawing from the principle of gravitational redshift and bringing it into quantum mechanical frameworks. The exploration looks through quantum mechanical relations and equations such as Planck-Einstein relation, De-Broglie’s relation and the relativistic wave equations, and propagators, accounting for the presence of gravitational fields through gravitational redshift of its momentum.

This study provides an in-depth exploration and analysis of the complex aspects of Public Key Cryptography, focusing on the vulnerabilities, potential attack vectors, and the consequential impacts of key compromises. The discussion extends beyond the conventional technical paradigms, offering a holistic perspective that intertwines theoretical insights with practical implications, thereby contributing to a more comprehensive understanding of cryptographic security. The paper delves into the intricacies of brute-force attacks, elucidating the significance of key sizes, encryption algorithms, and the inherent resilience of cryptographic systems against such attacks. It further examines the ramifications of key compromises in Public Key Cryptography, highlighting the repercussions on confidentiality, integrity, trust, and legal and reputational standing. The study underscores the importance of maintaining the security and integrity of cryptographic keys and provides practical recommendations to mitigate the risks associated with key compromises. These include enhanced awareness and education, stringent protection of sensitive information, proactive risk management, strict compliance with regulations and standards, and the promotion of a security-centric culture. The insights gleaned from this study are pivotal in informing future research, policy development, cryptographic implementations, and the cultivation of secure practices, fostering a more secure, resilient, and ethical digital environment in the face of an evolving threat landscape. The contributions of this study are instrumental in advancing the field of cryptography and enhancing the overall understanding of the challenges and considerations inherent in implementing robust cryptographic practices.

We humans are natural-born engineers. As such, we model after machines not only isolated, naturally occurring systems, but also the basic laws of physics, sharing with machines a local-evolution-of-state `grammar'. However, previous work by the author casts doubt upon this mechanistic paradigm, suggesting that it is to blame for the stubbornness of many open problems in physics. Simple experiments are therefore proposed to identify `non-machines'. In one experiment, `non mechanistic correlations' in the spirit of Bell are sought in a pair of separated but previously coupled (macroscopic) chaotic systems. In another it is tested whether chaotic systems could fuzzily `remember their future' in the sense that a future binary perturbation applied to them could be inferred from their present behavior with probability>1/2. Chaotic systems are chosen as candidates because the long-time application of their (deterministic) mechanistic description is conceptually groundless: All scales are significant and mutually coupled in that regime, down to scales governed by QM, yet the quantum-classical transition remains inexplicable---if only due to the measurement problem. Similarly for so-called non-deterministic chaotic systems, modeled as such purely for defying a short-time deterministic mechanistic description. Should a non mechanistic signature be found in such simple systems, the implications for science as a whole and life sciences in particular cannot be overstated.

Graphene is perhaps the most prominent “Dirac material,” a class of systems whose electronic structure gives rise to charge carriers that behave as relativistic fermions. In multilayer graphene several crystal sheets are stacked such that the honeycomb lattice of each layer is displaced along one of the lattice edges. When subject to an external magnetic field, the scaling of the multilayer energy spectrum with the magnetic field, and thus the system’s thermodynamic behavior, depends strongly on the number of layers. With this in mind, we examine the performance of a finite-time endoreversible Otto cycle with multilayer graphene as its working medium. We show that there exists a simple relationship between the engine efficiency and the number of layers, and that the efficiency at maximum power can exceed that of a classical endoreversible Otto cycle.

Controllable, quantum-strong correlations of polarization states can be implemented with multi-photon independent states. Polarization-based photonic quantum correlations can be traced back to the overlap of the polarization Stokes vectors on the Poincaré sphere between two polarization filters. The quantum Rayleigh scattering prevents a single photon from propagating in a straight line inside a dielectric medium, and it also provides a mechanism for the projective measurement of polarization. Complexities associated with single-photon sources and detectors can be eliminated because the quantum Rayleigh scattering in a dielectric medium destroys entangled photons. Entanglement-free, identical sources and processing devices give rise to correlations rather than these being caused by “quantum nonlocality”. These analytic developments were prompted by the vanishing expectation values of the Pauli spin vector for a single photon of maximally entangled photonic Bell states.

Decoherence with recurrences appear in the dynamics of the one-body density matrix of an $F = 1$ spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, that breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations very accurate time evolution of large condensates are analyzed, leading to heuristic analytic expressions for the time dependence of the density matrix, in the weak and strong interacting regimes. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, that show remarkable differences depending on the strength of the spin-spin interactions. We discuss the nature of these limits in the light of the thermodynamic limit.

Image synthesis poses a challenging problem that researchers in computer vision and machine learning have been grappling with for several decades. Numerous machine learning techniques have emerged and proven effective in generating high-fidelity artificial images. This study breaks new ground by exploring image synthesis through generative learning using the D-Wave 2000Q quantum annealer, marking the first attempt to address the issue of generative image synthesis on a Quantum Processing Unit (QPU). Alongside executing image synthesis on the quantum annealer, this research also compares its performance with existing classical models and delves into resolving the Generative Learning Trilemma.

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

Quantum mechanics, despite its remarkable empirical success, has been subject to longstanding interpretational challenges. This work introduces the Prescribed Observation Problem (POP) framework, which derives the complete formulation of quantum theory from the empirical basis of measurement outcomes, treated as an optimization constraint. Rather than postulating quantum principles axiomatically, the POP framework formulates quantum mechanics as the solution to an entropy maximization problem subject to this constraint, resulting in quantum theory's axioms emerging as theorems – the optimal, least biased probability measure consistent with the given measurement data. Notably, the POP framework is sufficiently powerful to reduce the foundation of quantum mechanics to a single axiom. Conventionally, interpretations of quantum mechanics need only align with the theory's postulated axioms, allowing for a plurality of viable interpretations that cannot definitively rule each other out. In contrast, the POP framework derives the axioms as theorems directly from empirical first principles, grounding them in observational constraints from the outset. This substantially restricts the allowable theoretical landscape, imposing stringent requirements for the viability of interpretations and invalidating all those that contradict this genesis. By engendering quantum theory from a formal empirical footing, the POP framework offers a compelling resolution to the enduring interpretational puzzles that have long plagued the field, effectively eliminating all but one interpretation consistent with both the axioms and their empirical genesis.

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators consisting of non-commuting variables. Thanks to the hermicity constraints, we obtain positive-definite dis- tribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of innitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probabil- ity distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

By employing the stochastic extension of the Madelung quantum-hydrodynamic description within a discrete methodology, we establish a solution using the path integral approach to explore the progression of quantum states' superposition. This investigation aims to understand the eventual establishment of a stable end-state configuration amid the backdrop of gravitational background fluctuations. The model identifies the circumstances that lead to a limited range of interaction for the quantum potential, allowing for the emergence of sizeable, classically described macroscopic phenomena. The theory unveils the lowest achievable level of uncertainty in an open quantum system and investigate its congruence with the localized behaviors of macroscopic classical systems. The study examines agreements and differences with decoherence theory and the Copenhagen interpretation of quantum mechanics, and evaluates the impact of wave function decay on the measurement process.

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

In this paper, we investigate the Hawking radiation process by using the quantum tunneling phenomenon of massive spin-1 (W-bosons) and spin-0 particles from (2+1) dimensional Black Hoke with quintessential and magnetic field. For this purpose, using Hamilton-Jacobi ansatz, we apply the WKB approximation to the field equations of massive charged vector particles. We get the required tunneling rate of radiated particles and obtain their corresponding Hawking temperature $T_h$. In order to study the quantum gravity effects, we utilize the generalized Proca and Klein-Gordan equations incorporating the generalized uncertainty principle (GUP) and recover the accompanying quantum corrected temperature $T'_{h}$.

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.

Maximal quantum correlations of unity do not violate the CSHS-Bell inequalities because the remaining two correlations vanish. The probability of coincident detections should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed. © The Author 2023

We communicate the theoretical results in the study of utilizing the quantum phenomena in optical current for quantum computation in the context of high precision voltage measurements. These results can be used around computation by quantum sampling and quantum communication as the basis for further research and physical implementations. We propose a Main Optical Setup (MOS) for such computation which allows to make a superstructure to implement specific computations and algorithms. To create MOS we used the nonlinear units (e.g., beta- barium borate crystal), arranged in series, powered with pulsed laser pump, and ended with the beam splitter to generate the output state of a number of entangled photon pairs. The computation is made by propagation of entanglement with beam splitters applied crossword and adjustable phase shifters that are tools for parameter steering. We show how to implement the series of cosine-based components on the example of two-component case. The results opens a broad area for future research in the area of building quantum optimizer using the quantum sampling methods and in the area of high precision temporal measurement of voltage, which is the important process for building high-fidelity devices.

In quantum approaches to consciousness, the authors try to propose a model and mechanism for the mind-brain interaction using modern physics and some quantum concepts which do not exist in the classical physics. The independent effect of mind on the brain has been one of the challenging issues in the history of science and philosophy. In some recent mind-brain interaction models, the direct influence of mind on matter is either not accepted (as in Stapp’s model) or not clear, and there have not been any clear mechanism for it (as in Penrose-Hameroff’s model or in Eccles’s model). In this manuscript we propose a model and mechanism for mind’s effect on the matter using an extended Bohmian quantum mechanics and Avicenna’s ideas. We show that mind and mental states can affect brain’s activity without any violation of physical laws. This is a mathematical and descriptive model which shows the possibility of providing a causal model for mind’s effect on matter. It is shown that this model guarantees the realistic philosophical constraints and respects the laws of nature. In addition, it is shown that it is in agreement with the Libet style experimental results and parapsychological data. To propose this model, we obtained a modified (non-unitary) Schrödinger equation via second quantization method which affects the particle through a modified quantum potential and a new term in the continuity equation. At the second quantized level, which is equivalent to quantum field theory level (QFT), we can use the path integral formalism of Feynman. We show that there are three methods to extend Bohmian QM via path integral formalism, which has different interpretations. By numerical simulation of trajectories in the two-slits experiment, we show their differences and choose one of these methods for our mind-brain model which can be the basis for explaining some phenomena which are not possible to explain in the standard Bohmian QM.

By expressing the Schrödinger wave function in the form $\psi =R{e}^{iS/\hslash }$ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., $V_Q=-\frac{{\hslash }^2}{2m}\frac{{\nabla }^{2}R}{R}$ , we have obtained a spin potential $V_S=-\frac{S{\nabla }^{2}S}{m}$ that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $m{c}^2$ with an internal frequency of $2m{c}^2/\hslash$ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

Quantum loops are processes that constitute quantum objects. In the causal model of quantum loops and quantum objects presented here, the nonlinear processes involve the elementary units of spacetime and the associated elementary units of quantum fields. As such, quantum loop processes are the sources of gravitational fields (i.e., spacetime curvature) and of the quantum objects wave function. The model may be viewed as a derivative of loop quantum gravity, spin networks and causal dynamical triangulation, although significant deviations to these theories exist. The causal model of quantum loops is based on a causal model of spacetime dynamics where space(-time) consists of interconnected space points, each of which is connected to a small number of neighboring space points. The curvature of spacetime is expressed by the density of these space points and by the arrangement of the connections between them. The quantum loop emerges in a nonlinear collective behavioral process from a collection of space points that carry energy and quantum field attributes.

In this letter, it is proposed that cryogenic quantum bits could operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated and the sensitivity of quantum bit frequency and anharmonicty with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process could reveal the expected properties, thus putting the context of quantum computing hardware into new perspectives.

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

We report the use of Einstein rings to reveal the quantized and dynamical states of space-time in a region of impressed gravitational field as predicted by the Nexus Paradigm of quantum gravity. This in turn reveals the orbital speeds of objects found therein and the radius of curvature of the quantized space-time. Similarities between the Nexus graviton and the singular isothermal sphere (SIS) in the Cold Dark Matter (CDM) paradigm are highlighted. However unlike the singular isothermal sphere, the Nexus graviton does not contain singularities or divergent integrals. This solves the core cusp problem. In this work, data from a sample of fifteen Einstein rings published on the Cfa-Arizona Space Telescope Lens Survey (CASTLES) website is used to probe the quantized properties of space-time.

In our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, e_n=2.95e and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. The aim of this paper is associated with understanding the mystery of quantum of magnetic flux, Planck’s quantum radiation constant and Reduced Planck’s constant. Proceeding further, quark charges, strong coupling constant, nuclear stability, nuclear binding energy, medium and heavy atomic X-ray levels and celestial magnetic moments can be understood in a unified approach. It may also be noted that, by considering integral nature of elementary particle masses, it seems possible to understand the discreteness of angular momentum. Considering our proposed e_n=2.95e=3e as a characteristic nuclear charge, it seems possible to understand the integral nature of quarks electromagnetic charge. With this idea, neutron, proton and pions decay can be understood very easily. In all the cases, up quark of charge (±2e) seems to play a crucial role with the internal transformation of down quark of charge (±e) and external observable elementary basic elementary particles. It needs further study at fundamental level.

We present a new perspective of the link between QED and Maxwell's equations. We demonstrate that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter, runs as it should.

Spontaneous parametric downconversion At the heart of all quantum optics experiments is called as Spontaneous parametric downconversion. This is a downconversion process when the output frequency is smaller than the input frequency. The whole process is Spontaneous. Experimentally we have to downconvert the photons and convert them into pairs of a photon. We use the Beta-barium borate(BBO) crystals to downconvert the coming violet-blue laser. We find the maximum number of counts on detectors and their coincidence. When the BBO crystals is well aligned, we find no difference in detecting vertically or horizontally polarized photons because they are orthogonal to each other. Proof of existence of photons We want to investigate the properties and verification of quantization of light. Experimently we want to establish the existence of single photon which shows the grainy-ness of individual photon quantum mechanically and shows wave like behaviour classically. We get the coincidences counts on detectors with addition of detector B’ by using PBS in the path of signal beam. Experimentally we prove the Quantum as well as classical nature of light by the measurement of second-order degree coherence in light g²(0). For classically the g²(0)≥1 and quantum mechanically g²(0)=0.When we add the delay time interval of 1ns after reflected and transmitted photons from PBS signal beam. The delay generator did not create a significant difference in the coincidence counts detection in the value of g²(τ ). Single photon interference and quantum eraser we want to observe the interference by making the single photons pass through the interferometer, and we will see the interference of the single photons. If the light passes through the interferometer, the visibility of the interference pattern to which extent these fringes are observed is dependent on the extent to which the ’which-way’ or ’which-path’ information is available to the experimenter. If the observer knows the information about the ’which-way’ of the light path, then we cannot observe the inference pattern. Because we only can make an interference pattern if we erase the which-way information of the light path. If you erase the information about the’ which-way,’ we can observe a very high interference pattern. We can erase the information about the light path’s ’which-way’ or ’which-path’ by using a polarizer and orienting at 45^o. In this way, we can observe a very high pattern. If we introduce the angle of the polarizer at 0^o or 90^o, we see very low interference.

This study presents the B92 Quantum Key Distribution scheme and its optimization and implementation considerations. Simulation software was developed to model and analyze the B92 protocol under varying conditions. Another contribution of this work is investigating how this protocol runs on real quantum computing hardware. New eavesdropping schemes were proposed and modeled.

The recent Google’s claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr’s principle of complementarity¹ (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd’s calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n). Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the denition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

In a recent paper \cite{Landsman1}, it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is {\it 1-random}. We also defend the correctness of this claim and assert that the outcomes of quantum measurements can be considered as an infinite {\it 1-random} or {\it n-random} sequence. In this brief note we present our comments on this claim. We have mostly positive but also some negative comments on the arguments of the paper \cite{Landsman1}. Furthermore, we speculate a logical-axiomatic study of nature which we believe can intrinsically provide quantum mechanical probabilities based on {\it 1(n)-randomness}.

On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof.

Variability is the predisposition of the elements in systems to assume different values over time and space. In biology, the variability is basic to explain differences and development in organisms but in the fields of scientific and technological information, the effects of variability on evolutionary dynamics of disciplines and technologies are unknown. In a broad analogy with the principles of biology, the variability within research fields can be a central argument to explain trajectories in scientific development and technological evolution. The purpose of the present study is to see whether statistical evidence supports the general hypothesis that the rate of growth in technologies can be explained by the level of variability in scientific fields and with this principal goal to analyze the relation between scientific variability and rate of growth in technologies. Proposed hypothesis of scientific variability here endeavors to explain basic sources of scientific development and technological evolution to lay the foundations for a general theory. The test here is based on emerging research fields of quantum technologies: Quantum Imaging, Quantum Meteorology, Quantum Sensing and Quantum Optics. A preliminary statistical evidence seems in general to support the hypothesis stated that the rate of growth in technological fields can be explained by the level of scientific variability in research fields, measured with relative entropy index. Nonparametric correlation based on Spearman’s rho shows a positive coefficient of 0.80 of these variables; linear model of the rate of technological growth = f(scientific variability) reveals a coefficient of regression equal to 1.63 (R²=0.60). Findings here suggest a general law that scientific variability positively drives scientific development and technological evolution. In particular, a higher variability within research fields can support scientific development and a high rate of growth in technological evolution (measured with scientific and technological information). Proposed hypothesis of scientific variability is especially relevant in environments of rapid change to explain determinants and dynamics of technological change within a general theoretical framework that supports technological management and forecasting of promising innovations.

We present the mathematical model of cooperative functioning of unconscious and consciousness. The model is based on the theory of open quantum systems. Unconscious and consciousness are treated as bio-information systems. The latter plays the role a measurement apparatus for the former. States of both systems are represented in Hilbert spaces. Consciousness performs measurements on the states which are generated in unconscious. This process of unconscious-conscious interaction is described by the scheme of indirect measurements. This scheme is widely used in quantum information theory and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). Our approach is known as quantum-like modeling. It should be sharply distinguished from modeling of genuine quantum physical processes in biosystems, in particular, in the brain. In the quantum-like framework, the brain is a black box processing information in the accordance with the laws of quantum theory. During the last 10-15 years this framework has been actively used in cognition, psychology, decision making, social and political sciences. The quantum-like scheme of unconscious-consciousness functioning has already been explored for sensation-perception modeling.

The evolutionary systems (ES) include software applications that solve problems using heuristic methods instead of the deterministic ones. The classical computing used for ES development involves random methods to improve different kinds of genomes. The mappings of these genomes lead to individuals that correspond to the searched solutions. The individual evaluations by simulations serve for the improvement of their genotypes. Quantum computations, unlike the classical computations, can describe and simulate a large set of individuals simultaneously. This feature is used to diminish the time for finding the solutions. Quantum Petri Nets (QPNs) can model dynamical systems with probabilistic features that make them appropriate for the development of ES. Some examples of ES applications using the QPNs are given to show the benefits of the current approach.

Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role for extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data, to 2-D image data, to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.