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arXiv:1503.05940 · Physical Review E

Dephasing and dissipation in qubit thermodynamics

Jukka P Pekola, Y. MASUYAMA, Yasunobu Nakamura, Joakim Bergli, Y. M. Galperin

Published Jun 8, 2015• 14 citations
arXivHTMLPDF

Abstract

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctuation relations (FRs) of nonequilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy U, leads to deviations in FRs under the same conditions. We relate the average 〈e(-βU)〉 (where β is the inverse temperature) with the qubit's relaxation and dephasing rates in the weak dissipation limit and discuss this relationship for different mechanisms of decoherence.

DOI
10.1103/physreve.91.062109

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The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations.They are promising tools to benchmark quantum devices and measure free energy differences.While they are well established theoretically and also experimental realizations for few-body systems already exist, their experimental validity in the quantum many-body regime has not been observed so far.Here, we present results for nonequilibrium protocols in systems with up to 16 interacting degrees of freedom obtained on trapped ion and superconducting qubit quantum computers, which test the quantum Jarzynski equality and the Crooks relation in the many-body regime.To achieve this, we overcome present-day limitations in the preparation of thermal ensembles and in the measurement of work distributions on noisy intermediate-scale quantum devices.We discuss the accuracy to which the Jarzynski equality holds on different quantum computing platforms subject to platformspecific errors.The analysis reveals the validity of Jarzynski's equality in a regime with energy dissipation, compensated for by a fast unitary drive.This provides new insights for analyzing errors in many-body quantum simulators.
A central challenge in quantum thermodynamics is to access work fluctuations in coherent processes without distorting the energetics of the unmeasured evolution. In standard two-point schemes, the initial energy measurement dephases coherent inputs, causing the measured average work to differ from that of the unmeasured evolution. Here, we develop an operational scheme for accessing work statistics for closed quantum systems based on the abstract notion of variation in the Heisenberg picture Hamiltonian. This scheme preserves energetically relevant coherences, thereby faithfully reproducing unmeasured work, while still producing positive probabilities. We derive modified Jarzynski and Crooks relations, as well as a thermodynamic uncertainty relation, identifying coherence-induced correction terms. Furthermore, we show that this scheme can reliably quantify the performance of a coherent engine in situations where the two-point energy measurement would suppress work output. In addition, the scheme requires only a single measurement and can predict the work associated with a subsequent unitary transformation. We exploit this feature to construct a Maxwell-demon protocol that can outperform energy-based feedback engines for coherent work extraction. Our results establish this scheme as a framework for accessing coherent work fluctuations without erasing the coherence that drives quantum thermodynamic performance.