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arXiv:1803.10053 · Fundamental theories of physics

Thermodynamic Principles and Implementations of Quantum Machines

Arnab Ghosh, Wolfgang Niedenzu, Victor Mukherjee, Gershon Kurizki

Published Jan 1, 2018• 13 citations
arXivHTMLPDF
DOI
10.1007/978-3-319-99046-0_2

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We present a thermodynamic analysis of a quantum engine that uses a single quantum particle as its working fluid, inspired by Szilard's classical single-particle engine. Our design is modeled after the classically-chaotic Szilard Map and involves a thermodynamic cycle of measurement, thermal-energy extraction, and memory reset. Our focus is on investigating the thermodynamic costs associated with observing and controlling the particle and comparing these costs in the quantum and classical limits. Through our study, we aim to shed light on the thermodynamic trade-offs that arise from Lindauer's Principle for information-processing-induced thermodynamic dissipation in both the quantum and classical regimes. Using machine learning methods, we demonstrate that energy analysis can be performed and the quantum engine can be simulated according to the Szilard engine based Second Law of Thermodynamics in its working condition. However, we note that the quantum engine operates using significantly different mechanisms than its classical counterpart, where the cost of inserting partitions plays a critical role in the quantum implementation.
We demonstrate how a single heat exchange between a probe thermal qubit and multiqubit thermal machine encoding a Boolean function can determine whether the function is balanced or constant, thus providing a thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore a restricted Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the three-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting that quantum thermodynamics could provide an unconventional route to computing beyond classical computation.