Adaptive variational simulation for open quantum systems

Huo Chen, Niladri Gomes, Siyuan Niu, and Wibe Albert de Jong

Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Emerging quantum hardware provides new possibilities for quantum simulation. While much of the research has focused on simulating closed quantum systems, the real-world quantum systems are mostly open. Therefore, it is essential to develop quantum algorithms that can effectively simulate open quantum systems. Here we present an adaptive variational quantum algorithm for simulating open quantum system dynamics described by the Lindblad equation. The algorithm is designed to build resource-efficient ansatze through the dynamical addition of operators by maintaining the simulation accuracy. We validate the effectiveness of our algorithm on both noiseless simulators and IBM quantum processors and observe good quantitative and qualitative agreement with the exact solution. We also investigate the scaling of the required resources with system size and accuracy and find polynomial behavior. Our results demonstrate that near-future quantum processors are capable of simulating open quantum systems.

Quantum computers hold the promise of being able to efficiently simulate other quantum systems, a critical application known as quantum simulation. Quantum simulation is not just of theoretical interest but is key to many technological applications, such as the design of artificial quantum systems for light harvesting, sensing, and energy storage. However, real-world quantum systems often interact with their environment, turning the system into what's known as an “open quantum system”. Therefore, it is essential to develop quantum algorithms that can effectively simulate open quantum systems.

In our work, we present a compact approach for simulating the open-quantum-system dynamics using a time-dependent adaptive variational method. The proposed algorithm constructs resource-efficient ansätze through the dynamical addition of operators by maintaining the simulation accuracy, providing a NISQ-friendly (Noisy Intermediate-Scale Quantum) alternatives to existing algorithms. We put this algorithm to the test on both noiseless simulators and actual IBM quantum processors, and the results exhibit good agreement with the exact solutions. Additionally, we demonstrate that the necessary resources scale reasonably with the increase in system size and precision.

Our results suggest that near-future quantum processors are capable of simulating open quantum systems. As quantum hardware continues to improve, we anticipate that our algorithm will open up new avenues for the practical simulation of open quantum systems in the NISQ era.

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