# Hardware-efficient quantum algorithm for the simulation of open-system dynamics and thermalisation

## TL;DR

This paper introduces a quantum algorithm that efficiently simulates open-system dynamics and thermalisation using a minimal number of qubits by reproducing reservoir correlation functions, enabling practical quantum simulations of complex environments.

## Contribution

The authors propose a novel method to simulate open-system dynamics with fewer qubits by reproducing reservoir correlation functions, reducing resource requirements for quantum simulations.

## Key findings

- Efficient simulation of open-system dynamics with fewer qubits.
- Reproduction of up to n-time correlation functions for master equation simulation.
- Environment size can be smaller than the system in the algorithm.

## Abstract

The quantum open-system simulation is an important category of quantum simulation. By simulating the thermalisation process at the zero temperature, we can solve the ground-state problem of quantum systems. To realise the open-system evolution on the quantum computer, we need to encode the environment using qubits. However, usually the environment is much larger than the system, i.e. numerous qubits are required if the environment is directly encoded. In this paper, we propose a way to simulate open-system dynamics by reproducing reservoir correlation functions using a minimised Hilbert space. In this way, we only need a small number of qubits to represent the environment. To simulate the $n$-th-order expansion of the time-convolutionless master equation by reproducing up to $n$-time correlation functions, the number of qubits representing the environment is $\sim \lfloor \frac{n}{2} \rfloor \log_2(N_\omega N_\beta)$. Here, $N_\omega$ is the number of frequencies in the discretised environment spectrum, and $N_\beta$ is the number of terms in the system-environment interaction. By reproducing two-time correlation functions, i.e. taking $n = 2$, we can simulate the Markovian quantum master equation. In our algorithm, the environment on the quantum computer could be even smaller than the system.