Thermal Efficiency of Quantum Memory Compression

Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the limit of asymptotically infinite parallel simulation. Comparing this cost with the classical regime reveals that quantizing classical simulators not only results in memory compression but also in reduced dissipation. We explore this advantage across a suite of representative examples.

[1]  James P. Crutchfield,et al.  Thermodynamically-Efficient Local Computation and the Inefficiency of Quantum Memory Compression , 2020 .

[2]  Renato Renner,et al.  Smooth Renyi entropy and applications , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[3]  M. Tomamichel.  A framework for non-asymptotic quantum information theory , 2012, 1203.2142.

[4]  M. Gu,et al.  Practical Unitary Simulator for Non-Markovian Complex Processes. , 2017, Physical review letters.

[5]  M. Horodecki,et al.  Fundamental limitations for quantum and nanoscale thermodynamics , 2011, Nature Communications.

[6]  Nicolai Friis,et al.  Ideal Projective Measurements Have Infinite Resource Costs , 2018, Quantum.

[7]  James P. Crutchfield,et al.  Equivalence of History and Generator-Machines , 2012 .

[8]  Johan Aberg,et al.  The thermodynamic meaning of negative entropy , 2011, Nature.

[9]  Karoline Wiesner,et al.  Quantum mechanics can reduce the complexity of classical models , 2011, Nature Communications.

[10]  R. Renner,et al.  The minimal work cost of information processing , 2012, Nature Communications.

[11]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[12]  Michal Horodecki,et al.  The second laws of quantum thermodynamics , 2013, Proceedings of the National Academy of Sciences.

[13]  F. Brandão,et al.  Resource theory of quantum states out of thermal equilibrium. , 2011, Physical review letters.

[14]  T. J. Elliott,et al.  Optimal stochastic modeling with unitary quantum dynamics , 2018, Physical Review A.

[15]  J. Anders,et al.  Quantum thermodynamics , 2015, 1508.06099.

[16]  James Odell,et al.  Between order and chaos , 2011, Nature Physics.

[17]  David Jennings,et al.  Description of quantum coherence in thermodynamic processes requires constraints beyond free energy , 2014, Nature Communications.

[18]  James P Crutchfield,et al.  Time's barbed arrow: irreversibility, crypticity, and stored information. , 2009, Physical review letters.

[19]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[20]  M. Lostaglio.  An introductory review of the resource theory approach to thermodynamics , 2019, Reports on progress in physics. Physical Society.

[21]  James P. Crutchfield,et al.  A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression , 2015, ArXiv.

[22]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[23]  R. Renner,et al.  Inadequacy of von Neumann entropy for characterizing extractable work , 2011 .

[24]  Renato Renner,et al.  Security of quantum key distribution , 2005, Ausgezeichnete Informatikdissertationen.

[25]  R. Renner,et al.  Inadequacy of von Neumann entropy for characterizing extractable work , 2009, 0908.0424.

[26]  James P. Crutchfield,et al.  Occam’s Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel , 2015, Scientific Reports.

[27]  James P. Crutchfield,et al.  Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes , 2018, Journal of Statistical Physics.

[28]  Jayne Thompson,et al.  Using quantum theory to simplify input–output processes , 2016, npj Quantum Information.

[29]  H. Wiseman,et al.  Observing the ambiguity of simplicity via quantum simulations of an Ising spin chain , 2017, 1711.03661.

[30]  D. Janzing,et al.  Thermodynamic Cost of Reliability and Low Temperatures: Tightening Landauer's Principle and the Second Law , 2000, quant-ph/0002048.

[31]  James P. Crutchfield,et al.  Above and Beyond the Landauer Bound: Thermodynamics of Modularity , 2017, Physical Review X.

[32]  Matteo Lostaglio,et al.  An introductory review of the resource theory approach to thermodynamics , 2018, Reports on progress in physics. Physical Society.

[33]  Howard M Wiseman,et al.  Experimentally modeling stochastic processes with less memory by the use of a quantum processor , 2017, Science Advances.

[34]  'Alvaro M. Alhambra,et al.  Fluctuating Work: From Quantum Thermodynamical Identities to a Second Law Equality , 2016, 1601.05799.

[35]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[36]  Marco Tomamichel,et al.  Chain Rules for Smooth Min- and Max-Entropies , 2012, IEEE Transactions on Information Theory.

[37]  Daniel Ray Upper,et al.  Theory and algorithms for hidden Markov models and generalized hidden Markov models , 1998 .

[38]  James P. Crutchfield,et al.  Causal Asymmetry in a Quantum World , 2017, Physical Review X.

[39]  James P. Crutchfield,et al.  Many Roads to Synchrony: Natural Time Scales and Their Algorithms , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  L. Goddard.  Information Theory , 1962, Nature.

[41]  A. B. Boyd,et al.  Identifying functional thermodynamics in autonomous Maxwellian ratchets , 2015, 1507.01537.