Quantum Foundations of Classical Reversible Computing
arXiv:2105.00065 · doi:10.3390/e23060701
Abstract
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 digital 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.
arXiv comment73 pages, 16 figures, accepted by Entropy
References in corpus (48)
- Decoherence, einselection, and the quantum origins of the classical
- Rényi Divergence and Kullback-Leibler Divergence
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Quantum Resource Theories
- Shortcuts to adiabaticity: concepts, methods, and applications
- The role of quantum information in thermodynamics --- a topical review
- Fundamental limitations for quantum and nano thermodynamics
- Fluctuation theorems: Work is not an observable
- On quantum Renyi entropies: a new generalization and some properties
- The second laws of quantum thermodynamics
- Assessing non-Markovian dynamics
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Symmetries and conserved quantities in Lindblad master equations
- An improved Landauer Principle with finite-size corrections
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Dividing Quantum Channels
- Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
- An introductory review of the resource theory approach to thermodynamics
- Thermodynamics of precision in quantum non equilibrium steady states
- Stochastic thermodynamics of computation
- Analysis of quantum semigroups with GKS--Lindblad generators II. General
- Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
- alpha-z-relative Renyi entropies
- A non-equilibrium quantum Landauer principle
- Geometry and response of Lindbladians
- Thermodynamic and Logical Reversibilities Revisited
- Ideal Projective Measurements Have Infinite Resource Costs
- Quantum work and the thermodynamic cost of quantum measurements
- Information preserving structures: A general framework for quantum zero-error information
- Non-Markovianity and negative entropy production rates
- Thermodynamic length in open quantum systems
- Necessary and Sufficient Conditions for the Trumping Relation
- Catalytic Conversion Probabilities for Bipartite Pure States
- Correlating thermal machines and the second law at the nanoscale
- Stochastic thermodynamics with information reservoirs
- Information scrambling vs. decoherence -- two competing sinks for entropy
- Code properties from holographic geometries
- Holographic Bound From Second Law of Thermodynamics
- Mechanical Computing Systems Using Only Links and Rotary Joints
- Work and entropy production in generalised Gibbs ensembles
- Reversible Fluxon Logic: Topological particles allow ballistic gates along 1D paths
- Structure of Uniformly Continuous Quantum Markov Semigroups
- Relative Entropy and Catalytic Relative Majorization
- Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems
- Full counting statistics approach to the quantum non-equilibrium Landauer bound
- Reversible Fluxon Logic with optimized CNOT gate components
- Negative entropy production rates in Drude-Sommerfeld metals
- Evaluating the Friction of Rotary Joints in Molecular Machines