Process Tensors Enable Exact Quantum Work Statistics for Driven Open Quantum Systems

Quantifying the energy costs of operations represents a fundamental challenge in developing practical quantum technologies, particularly when devices operate rapidly and interact with complex environments. Mike Shubrook, Moritz Cygorek from Technical University of Dortmund, Erik Gauger from Heriot-Watt University, and colleagues now present a new method for calculating these energy costs with unprecedented accuracy. The team developed a process tensor framework that allows researchers to determine the full probability distribution of energy exchange in driven quantum systems, even when conventional approximations fail. This approach reveals subtle quantum effects missed by simpler calculations and significantly improves understanding of protocols like Landauer’s erasure, offering a powerful tool for optimising the performance of both current and future quantum devices.

Quantum Work Measurement and Thermodynamics at Scale

This research investigates quantum thermodynamics, focusing on how thermodynamic principles apply to quantum systems. Traditional thermodynamics breaks down at the nanoscale, necessitating new approaches to understand energy transfer and work. Scientists are particularly interested in the probability distribution of work done during a quantum process and how it deviates from classical expectations. This work relies heavily on developing and validating computational methods to accurately calculate these work distributions in complex quantum systems, especially those interacting with their environment.

The research develops theoretical frameworks and computational tools to address these challenges. A common approach involves the two-point measurement technique, defining work by measuring the system’s initial and final states. Quantum trajectory methods simulate the time evolution of quantum systems, including environmental interactions. The work characteristic function, a mathematical tool representing the work distribution, is often used, as it’s easier to calculate and then reconstruct the distribution. Significant effort focuses on developing efficient computational methods, such as generalized-time step methods for solving the time-dependent Schrödinger equation.

The results demonstrate accurate work distribution calculations for complex quantum systems, including those open to environmental interactions. Simulations validate the theoretical frameworks used to define and measure work in quantum mechanics, contributing to a better understanding of non-equilibrium thermodynamic processes. This work has potential applications in diverse fields, including the design and optimization of quantum technologies, understanding energy transfer at the nanoscale, studying energy transduction in biological systems, and designing new materials with tailored thermodynamic properties.

Process Tensor Framework for Quantum Work Calculation

Scientists have developed a process tensor framework to accurately quantify the thermodynamic work costs of quantum operations, overcoming limitations in rapidly controlled, non-equilibrium quantum systems. This achievement enables the computation of complete quantum work statistics for driven open quantum systems, surpassing the accuracy of conventional approximations. The core innovation lies in a novel method for propagating the work characteristic operator, unifying physical time and a counting field onto a single generalized-time axis, simplifying complex calculations. To implement this approach, researchers constructed forward and backward propagating Hamiltonians, evolving the work characteristic operator using a non-completely-positive, trace-preserving map.

This propagation relies on discretizing the generalized-time axis and applying a Trotter decomposition. By leveraging matrix product operator techniques, specifically process tensor methods, the team efficiently represents and propagates the system dynamics, capturing non-Markovian correlations. This allows for numerically exact results for the complete work statistics of driven open quantum systems, establishing a powerful tool for exploring thermodynamics and control in both near-term and future quantum devices.

Process Tensors Map Quantum Work Statistics

This research introduces a process tensor framework for calculating the complete statistics of quantum work, a crucial step for optimizing quantum technologies. Scientists developed a method to accurately determine the energetic costs of quantum operations, even in complex and rapidly changing environments where traditional approximations fail. The team computed work probability distributions for a Landauer erasure protocol, revealing quantum signatures previously missed by simpler calculations. The breakthrough centers on a novel approach to tracking energy exchange, utilizing a “process tensor” to map complex quantum dynamics onto a single, generalized time axis.

This allows for numerically exact calculations of work statistics, overcoming limitations of existing methods. By implementing a “shortcut to adiabaticity,” the team demonstrated the ability to suppress unwanted transitions that degrade performance, even with strong environmental interactions. Experiments revealed that the full work probability distribution contains rich structural information, including signatures of non-adiabatic coherences that adversely affect erasure fidelity. The framework delivers non-perturbative accuracy, meaning it doesn’t rely on approximations that limit its precision. This allows researchers to explore the thermodynamics and control of both current and future quantum devices with unprecedented detail. The method utilizes process-tensor matrix-product-operator techniques, enabling numerically exact dynamics and providing a powerful tool for understanding energy fluctuations in complex quantum systems.

Landauer Erasure via Process Tensor Dynamics

This research presents a numerically exact framework for calculating the complete statistics of work transfer in driven, open quantum systems, addressing a significant challenge in regimes of rapid control and complex environments. The team developed a process tensor approach, enabling detailed characterization of energy exchange fluctuations without relying on approximations. This method involves constructing a work-counting process tensor and propagating it along a generalized time axis, allowing for the calculation of work distributions and moments with arbitrary accuracy. Demonstrating the utility of this framework, the researchers applied it to a Landauer erasure protocol, revealing rich structure in the work distribution at strong environmental coupling.

Notably, incorporating a system-time-dependent auxiliary component suppressed peaks associated with non-adiabatic qubit transitions, leading to improved erasure fidelity without altering low-order work moments. The versatility of this approach extends beyond specific protocols, offering a means to efficiently optimize work costs and performance metrics by simply redefining the system’s Hamiltonian. Future work could focus on incorporating alternative tensor-network techniques to extend the framework’s applicability to larger and more complex systems, and applying it to a wider range of quantum control protocols and system-environment interactions. This achievement is expected to be valuable for both quantum control and quantum thermodynamics, enabling access to previously challenging regimes and aiding in the identification of protocols that minimize work cost while maintaining high fidelity.