A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a nonequilibrium initial state. Boltzmann only replied ``then go and invert them''. This problem of the relationship between the microscopic and macroscopic descriptions of the physical world and time-reversibility has been hotly debated from the XIXth century up to nowadays. At present, no modern computer is able to perform Boltzmann's demand for a macroscopic number of particles. In addition, dynamical chaos implies exponential growth of any imprecision in the inversion that leads to practical irreversibility. Here we show that a quantum computer composed of a few tens of qubits, and operating even with moderate precision, can perform Boltzmann's demand for a macroscopic number of classical particles. Thus, even in the regime of dynamical chaos, a realistic quantum computer allows to rebuild a specific initial distribution from a macroscopic state given by thermodynamic laws.
Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'
最近，论文B。乔治和D.L. Shepelyansky，Phys. Rev. 86_，5393（2001）中提出的[C. Zalka，quant-ph/0110019; L. Di'osi，quant-ph/0110026]。这封信声称，当在量子计算机上执行Arnold猫映射下的相空间密度演化时，误差敏感性将呈指数级加速和降低。一方面，有些观点以前的答复者尚未提出。另一方面，作者的反应[quant-ph/0110142]提出了新的问题。本说明述及这两个问题。
Comment on "Entanglement and the Thermodynamic Arrow of Time" and Correct Reply on "Comment on "Quantum Solution to the Arrow-of-Time Dilemma"" of David Jennings and Terry Rudolph
Time Symmetry, Retrocausality and the Emergent: Arrow of Time the Quantum Time-Symmetric Interpretation (QTSI)
Instituto de Ciencias Nucleares (ICN), UNAM（墨西哥国立自治大学核科学研究所）；Centro de Ciencias de la Complejidad (C3), UNAM（墨西哥国立自治大学复杂科学中心）；El Colegio Nacional（国家学院）
Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates
Departamento de Fisica de Materia Condensada, GIYA, CAC-CNEA（凝聚态物理系，GIYA，CAC-CNEA）；Instituto de Nanociencia y Nanotecnologia, INN-CONICET-CNEA（纳米科学与技术研究所，INN-CONICET-CNEA）
Closed Quantum Boltzmann Bridges: Coherent Revivals, Hidden Microstates, and the Emergence of Classical Two-Time Entropy Conditioning
University of Western Ontario（韦仕敦大学）；National Research Council Canada（加拿大国家研究委员会）；Institut für Physik und Astronomie, Technische Universität Berlin（柏林工业大学物理与天文研究所）
Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons
University of Science and Technology of China（中国科学技术大学）；Tsinghua University（清华大学）；The Chinese University of Hong Kong（香港中文大学）；Hefei National Laboratory（合肥国家实验室）
