Quantum thermodynamic relationships in emerging nanodevices are significant but often complex to deal with. The application of machine learning in quantum thermodynamics has provided a new perspective. This study employs reinforcement learning to output the optimal cycle of a quantum heat engine. Specifically, the soft actor-critic algorithm is adopted to optimize the cycle of a three-level coherent quantum heat engine with the aim of maximal average power. The results show that the optimal average output power of the coherent three-level heat engine is 1.28 times greater than the original cycle (steady limit). Meanwhile, the efficiency of the optimal cycle is greater than the Curzon-Ahlborn efficiency as well as efficiencies reported by other researchers. Notably, this optimal cycle can be fitted as an Otto-like cycle, which illustrates the effectiveness of the method.
Quantum thermodynamic relationships in emerging nanodevices are significant but often complex to deal with. The application of machine learning in quantum thermodynamics has provided a new perspective. This study employs reinforcement learning to output the optimal cycle of a quantum heat engine. Specifically, the soft actor-critic algorithm is adopted to optimize the cycle of a three-level coherent quantum heat engine with the aim of maximal average power. The results show that the optimal average output power of the coherent three-level heat engine is 1.28 times greater than the original cycle (steady limit). Meanwhile, the efficiency of the optimal cycle is greater than the Curzon-Ahlborn efficiency as well as efficiencies reported by other researchers. Notably, this optimal cycle can be fitted as an Otto-like cycle, which illustrates the effectiveness of the method.
Abstract The optimal control of open quantum systems is a challenging task but has a key role in improving existing quantum information processing technologies. We introduce a general framework based on reinforcement learning to discover optimal thermodynamic cycles that maximize the power of out-of-equilibrium quantum heat engines and refrigerators. We apply our method, based on the soft actor-critic algorithm, to three systems: a benchmark two-level system heat engine, where we find the optimal known cycle; an experimentally realistic refrigerator based on a superconducting qubit that generates coherence, where we find a non-intuitive control sequence that outperforms previous cycles proposed in literature; a heat engine based on a quantum harmonic oscillator, where we find a cycle with an elaborate structure that outperforms the optimized Otto cycle. We then evaluate the corresponding efficiency at maximum power.
This research employs the Kraus representation and Sz.-Nagy dilation theorem to model a three-level quantum heat on quantum circuits, investigating its dynamic evolution and thermodynamic performance. The feasibility of the dynamic model is validated by tracking the changes of population. On the basis of reinforcement learning algorithm, the optimal cycle of the quantum heat engine for maximal average power is proposed and verified by the thermodynamic model. The stability of quantum circuit simulations is scrutinized through a comparative analysis of theoretical and simulated results, predicated on an orthogonal test. These results affirm the practicality of simulating quantum heat engines on quantum circuits, offering potential for substantially curtailing the experimental expenses associated with the construction of such engines.
A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on reinforcement learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal tradeoffs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.
A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on Reinforcement Learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal trade-offs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.
Quantum heat machines, encompassing heat engines, refrigerators, heaters, and accelerators, represent the forefront of quantum thermodynamics, offering a novel paradigm for converting heat energy into useful mechanical work. Leveraging quantum mechanical principles, these machines promise superior efficiency and performance compared to classical counterparts, with potential applications in renewable energy and quantum computing. This paper investigates a quantum Otto engine operating in both ideal and finite-time scenarios, employing a two-level system interacting with a harmonic oscillator within the framework of the anisotropic quantum Rabi-Stark model (AQRSM) as the working medium. This model is notable for exhibiting both first-order and continuous quantum phase transitions. By focusing on quantum heat engines, our study reveals that these phase transitions critically modulate the efficiency and power of AQRSM-based engines, outperforming quantum engines fueled by working medium with harmonic spectrum. Additionally, we explore the impacts of quantum friction and conduct limit cycle analysis in finite-time operations, providing insights into optimizing quantum heat engines for practical implementation.
Abstract We work on a comprehensive theoretical investigation of a three-level quantum heat engine operating with engineered squeezed thermal reservoirs. Unlike conventional quantum heat engines that use thermal reservoirs, we demonstrate that squeezed reservoirs can significantly enhance the engine's performance by increasing both efficiency and output power. Using a rigorous open-quantum-system approach, we derive the full Lindblad master equation for a three-level system interacting with hot and cold squeezed thermal baths. Through a detailed analysis of the steady-state thermodynamics, we obtain explicit expressions for heat currents, work output, and efficiency. Our results reveal that moderate squeezing parameters (r≈0.5) combined with optimal squeezing phase (ϕ=π/2) enhance the engine efficiency by up to 40\% compared to the classical Carnot limit for the same temperature ratio. The power output shows a non-monotonic behavior with squeezing, exhibiting an optimal squeezing parameter that maximizes performance. We identify three distinct operational regimes: (i) heat engine regime, (ii) refrigerator regime, and (iii) heat pump regime, which can be tuned by adjusting the squeezing phase. The efficiency at maximum power follows a universal scaling ηMP≈ηCarnot/2+Δη(r), where Δη(r) represents the squeezing-induced enhancement. Our findings provide fundamental insights into the role of non-thermal reservoirs in quantum thermodynamics and offer practical guidelines for designing high-performance quantum heat engines using squeezed light and engineered baths.