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arXiv:2106.04388 · PRX Quantum

Experimental Verification of Fluctuation Relations with a Quantum Computer

Andrea Solfanelli, Alessandro Santini, Michele Campisi

Published Sep 30, 2021• 63 citations

Abstract

Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far.In order to do so, we first put forward a novel method to implement the so called two-point measurement scheme, which is at the basis of the study of nonequilibrium energetic exchanges in quantum systems.Like previously established methods, our method uses an ancillary system, but at variance with them, it provides direct access to the energy exchange statistics, and is, accordingly more effective, at least when applied to small quantum systems.Using a quantum computer as a remotely programmable experimental platform, we first validate our ancilla-assisted two-point measurement scheme, and then apply it to (i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction, which was not validated so far; (ii) experimentally verify the so-called heat-engine fluctuation relation, by implementing a SWAP quantum heat engine; (iii) experimentally verify that the heat-engine fluctuation relation holds for measurement-fueled quantum heat engines, by implementing the design at the basis of the so-called quantum-measurement-cooling concept.For both engines, we report the measured average heat and work exchanged and single out their operation mode.Our experiments constitute an experimental basis for the understanding of the nonequilibrium energetics of quantum computation and for the implementation of energy-management devices on quantum processors.

DOI: 10.1103/prxquantum.2.030353

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We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid-state implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.

Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of quantum fluctuation relations do not account for quantum correlations and quantum coherence, two essential quantum properties. We here experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup. We confirm, in particular, individual integral fluctuation relations for quantum correlations and quantum coherence, as well as for the sum of all quantum contributions. These refined formulations of the second law are important for the investigation of fully quantum features in nonequilibrium thermodynamics.

The nonequilibrium fluctuation relation is a cornerstone of quantum thermodynamics. It is widely believed that the system-bath heat exchange obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this theorem is established in the Born-Markovian approximation under the weak-coupling condition. Via studying the energy exchange between a harmonic oscillator and its coupled bath in the non-Markovian dynamics, we establish a generalized quantum fluctuation theorem for energy exchange being valid for arbitrary coupling strength. The Jarzynski-Wójcik fluctuation theorem is recovered in the weak-coupling limit. We also find the average energy exchange exhibits rich nonequilibrium characteristics when different numbers of system-bath bound states are formed, which suggests a useful way to control the quantum heat. Deepening our understanding of the fluctuation relation in quantum thermodynamics, our result lays the foundation to design high-efficiency quantum heat engines.

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

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Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of quantum fluctuation relations do not account for quantum correlations and quantum coherence, two essential quantum properties. We here apply a novel dynamic Bayesian network approach to experimentally test detailed and integral fully quantum fluctuation theorems for heat exchange between two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup. We concretely verify individual integral fluctuation relations for quantum correlations and quantum coherence, as well as for the sum of all quantum contributions. We further investigate the thermodynamic cost of creating correlations and coherence.