Quantum computing promises exponential speedups for specific computational tasks compared to classical computing. However, the inherent fragility of quantum states—their susceptibility to decoherence—poses a significant challenge to realizing this potential. This work investigates the crucial role of non-equilibrium thermodynamics in governing the dynamics of quantum computation. It argues that the efficiency of quantum algorithms is fundamentally linked to the non-equilibrium interactions between the quantum system (qubits) and its environment. A novel thermodynamic framework is proposed, moving beyond the traditional assumptions of equilibrium. This framework utilizes concepts from non-equilibrium statistical mechanics to model energy transfer and information flow between qubits and the surrounding environment, offering a pathway to understand and potentially mitigate decoherence. Specifically, we introduce a quantum computing heat engine model, formulated using non-equilibrium statistical ensembles, to quantify the impact of environmental fluctuations on qubit coherence. The core claim is that a new thermodynamic understanding is required for optimal quantum algorithm design and control. Key mathematical concepts include the Boltzmann entropy, the Landau free energy, and the quantum master equation. The analysis highlights the need for sophisticated control strategies that actively manage environmental fluctuations rather than passively attempting to isolate the quantum system.
Quantum computing promises exponential speedups for specific computational tasks compared to classical computing. However, the inherent fragility of quantum states—their susceptibility to decoherence—poses a significant challenge to realizing this potential. This work investigates the crucial role of non-equilibrium thermodynamics in governing the dynamics of quantum computation. It argues that the efficiency of quantum algorithms is fundamentally linked to the non-equilibrium interactions between the quantum system (qubits) and its environment. A novel thermodynamic framework is proposed, moving beyond the traditional assumptions of equilibrium. This framework utilizes concepts from non-equilibrium statistical mechanics to model energy transfer and information flow between qubits and the surrounding environment, offering a pathway to understand and potentially mitigate decoherence. Specifically, we introduce a quantum computing heat engine model, formulated using non-equilibrium statistical ensembles, to quantify the impact of environmental fluctuations on qubit coherence. The core claim is that a new thermodynamic understanding is required for optimal quantum algorithm design and control. Key mathematical concepts include the Boltzmann entropy, the Landau free energy, and the quantum master equation. The analysis highlights the need for sophisticated control strategies that actively manage environmental fluctuations rather than passively attempting to isolate the quantum system.
This paper explores a novel approach to quantum computing by integrating the principles of non-equilibrium quantum thermodynamics with the design of a "quantum heat engine". The core idea is to harness energy transfer between quantum states to emulate quantum logic gates, offering a potentially new architecture for quantum computation. The theoretical framework utilizes non-equilibrium statistical mechanics, specifically focusing on the Landauer-Petri equation and the generalized Boltzmann equation, to describe the dynamics of quantum heat engines. This approach allows for precise control over energy transfer and, consequently, the execution of quantum algorithms. The paper details the mathematical formalism, including the definition of relevant thermodynamic potentials (Helmholtz, Gibbs, and Shannon), and explores the key parameters governing the performance of the proposed quantum heat engine. The central claim is that a carefully engineered quantum heat engine can serve as a platform for quantum computation. The core mechanism involves translating quantum logic operations into controlled energy transfer pathways. This work establishes a theoretical foundation for investigating this paradigm and highlights the potential for innovative quantum computing solutions.
Quantum computing promises revolutionary advancements across various fields, yet its practical realization is severely hampered by errors arising from various sources. Traditional approaches to error correction in quantum computing often treat decoherence and other error mechanisms as isolated processes. This paper proposes a novel framework for understanding and mitigating quantum computing errors by grounding them within the principles of non-equilibrium thermodynamics. We argue that quantum bit (qubit) errors are not solely due to decoherence, but are fundamentally linked to energy transfer and entropy generation within the quantum system. We develop a mathematical model based on non-equilibrium thermodynamics to describe the propagation of errors, considering the dynamic interactions between qubits and their environment. This model incorporates concepts such as the Boltzmann equation, the Fokker-Planck equation, and the Landauer principle. Specifically, we define error propagation as a non-linear diffusion process driven by thermal fluctuations and dissipation. The model predicts the evolution of the error distribution across a quantum processor, highlighting the critical role of temperature, coupling strengths, and dissipation rates in error propagation. Furthermore, we explore potential control strategies based on this thermodynamic framework, including tailored cooling schemes and optimized qubit interactions to minimize error propagation. The core claim of this work is that a comprehensive understanding of quantum computing errors necessitates a shift from purely quantum mechanical descriptions to a thermodynamic perspective, offering a pathway towards more robust and scalable quantum computers.
Quantum noise poses a significant challenge to the reliable operation of quantum technologies, particularly in quantum computing and quantum information processing. Traditional noise mitigation techniques often rely on cryogenic cooling and shielding, which can be resource-intensive and may not fully address the underlying noise mechanisms. This paper proposes a novel approach to quantum noise suppression based on precise control of the non-equilibrium thermodynamic relationship between a quantum system and its environment. The core idea is to utilize micro-heat sources and micro-cold sources to apply non-equilibrium thermal driving to the quantum system, effectively tuning its energy distribution and thereby reducing the density of noise energy. This approach leverages fundamental principles of thermodynamics to actively manage and mitigate quantum noise. The theoretical framework presented demonstrates a pathway to significantly extending coherence times in quantum bits (qubits) through this tailored non-equilibrium control. We explore the mathematical formalism underpinning this approach, highlighting the key equations governing the system's energy state and noise correlation. The efficacy of this strategy is discussed in terms of controlling the system's temperature and its impact on the quantum noise.
This paper presents an analysis of quantum Otto heat engines operating out of equilibrium. It explores the fundamental thermodynamic principles governing these engines, focusing on efficiency, work output, and the impact of environmental factors, including thermal gradients, external fields, noise, and decoherence. The study investigates the effects of non-equilibrium conditions on engine performance, highlighting challenges and opportunities in practical realizations. Through numerical simulations, the article examines the power, efficiency, and performance coefficients, revealing trade-offs between these metrics and the influence of temperature differences and internal coupling strength. The results demonstrate that non-equilibrium effects can significantly reduce efficiency compared to idealized scenarios, underscoring the importance of accounting for both quantum effects and real-world constraints in the design and optimization of quantum heat engines. This work contributes to the growing body of knowledge in quantum thermodynamics, offering insights for quantum computing, sustainable energy technologies, and thermodynamic cycles at the quantum scale.
Abstract This paper presents an analysis of quantum Otto heat engines operating in non-equilibrium. It explores the fundamental thermodynamic principles that govern these engines, focusing on efficiency, work output, and the impact of environmental factors such as thermal gradients, external fields, noise, and decoherence. The study investigates the effects of non-equilibrium conditions on engine performance, highlighting challenges and opportunities in practical realizations. Through numerical simulations, the article examines the power, efficiency, and performance coefficients, revealing trade-offs between these metrics and the influence of temperature differences and internal coupling strength. The results demonstrate that non-equilibrium effects can significantly reduce efficiency compared to ideal scenarios, emphasizing the importance of considering both quantum effects and real-world limitations in the design and optimization of quantum heat engines. This work contributes to the growing body of knowledge in quantum thermodynamics, offering insights for quantum computing, sustainable energy technologies, and thermodynamic cycles at the quantum scale.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.