Quantum simulation of correlated systems strongly coupled to environments

The dynamics of quantum systems that are strongly entangled with their environments require incorporating memory effects, which retain past correlations between the quantum system and the environment. Simulating such non-Markovian dynamics on classical computers is extremely demanding, since the computational cost generally increases exponentially with the simulation time. To overcome this limitation, the use of quantum computers and hybrid classical–quantum algorithms is expected to provide an efficient alternative framework.

We propose the Block-Lanczos Time-Evolving Block Decimation (BL-TEBD) method—an algorithm that compresses the information of quantum systems and can be directly extended to real quantum hardware. Based on the s-d model, we perform time evolution with BL-TEBD, setting an impurity in vacuum as the initial state and observing the formation process of the Kondo singlet as the final state. We also discuss the extensibility of BL-TEBD to quantum algorithms and touch on the possibility of reducing the exponentially growing cost of dynamical simulations to polynomial time.

This work constitutes a milestone in the development of hybrid classical–quantum algorithms aimed at applications in condensed matter physics, leveraging HPC techniques in the NISQ era.