Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Estimating Algorithmic Information using Quantum Computing for Genomics Applications

Version 1 : Received: 3 February 2021 / Approved: 4 February 2021 / Online: 4 February 2021 (12:04:02 CET)

A peer-reviewed article of this Preprint also exists.

Sarkar, A.; Al-Ars, Z.; Bertels, K. Estimating Algorithmic Information Using Quantum Computing for Genomics Applications. Appl. Sci. 2021, 11, 2696. Sarkar, A.; Al-Ars, Z.; Bertels, K. Estimating Algorithmic Information Using Quantum Computing for Genomics Applications. Appl. Sci. 2021, 11, 2696.

Journal reference: Appl. Sci. 2021, 11, 2696
DOI: 10.3390/app11062696

Abstract

Inferring algorithmic structure in data is essential for discovering causal generative models. In this research, we present a quantum computing framework using the circuit model, for estimating algorithmic information metrics. The canonical computation model of the Turing machine is restricted in time and space resources, to make the target metrics computable under realistic assumptions. The universal prior distribution for the automata is obtained as a quantum superposition, which is further conditioned to estimate the metrics. Specific cases are explored where the quantum implementation offers polynomial advantage, in contrast to an indispensable exhaustive enumeration in the corresponding classical case. The unstructured output data and the computational irreducibility of Turing machines make this algorithm impossible to approximate using heuristics. Thus, exploring the space of program-output relations is one of the most promising problems for demonstrating quantum supremacy using Grover search that cannot be dequantized. Experimental use cases for quantum acceleration are developed for self-replicating programs and algorithmic complexity of short strings. With quantum computing hardware rapidly attaining technological maturity, we discuss how this framework will have significant advantage for various genomics applications in meta-biology, phylogenetic tree analysis, protein-protein interaction mapping and synthetic biology. This is the first time experimental algorithmic information theory is implemented using quantum computation. Our implementation on the Qiskit quantum programming platform is copy-left and can be found on https://github.com/Advanced-Research-Centre/QPULBA

Keywords

algorithmic information theory; universal distribution; Kolmogorov complexity; quantum algorithms; quantum circuit model; quantum Turing machine; genomics; viral genomics; meta-biology

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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