Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Quantum Foundations of Classical Reversible Computing

Version 1 : Received: 30 April 2021 / Approved: 5 May 2021 / Online: 5 May 2021 (13:50:13 CEST)
Version 2 : Received: 5 May 2021 / Approved: 7 May 2021 / Online: 7 May 2021 (10:42:31 CEST)
Version 3 : Received: 27 May 2021 / Approved: 28 May 2021 / Online: 28 May 2021 (12:13:42 CEST)

How to cite: Frank, M.; Shukla, K. Quantum Foundations of Classical Reversible Computing. Preprints 2021, 2021050066. Frank, M.; Shukla, K. Quantum Foundations of Classical Reversible Computing. Preprints 2021, 2021050066.


The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.


non-equilibrium quantum thermodynamics; thermodynamics of computing; Landauer's principle; Landauer limit; reversible computing; resource theory of quantum thermodynamics; Gorini-Kossakowski-Sudarshan-Lindblad dynamics; von Neumann entropy; Rényi entropy; open quantum systems



Comments (1)

Comment 1
Received: 7 May 2021
Commenter: Michael Frank
Commenter's Conflict of Interests: Author
Comment: A few minor edits; the only major change is in sec., where we inserted a new introductory paragraph, and a new accompanying figure (new Fig. 7).  The new material does not affect the rest of the paper, but is important for explicitly clarifying the fundamental consistency between the treatment in sec. 2.2.2, and the broader framework that was presented in sec. 2.1.
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