# Assisted quantum simulation of open quantum systems

## TL;DR

This paper introduces quantum-assisted algorithms that leverage NISQ devices to simulate open quantum systems efficiently, reducing circuit depth and enabling practical quantum simulations on current hardware.

## Contribution

It proposes a novel quantum-assisted framework and specific algorithms for simulating open quantum systems with shallow circuits suitable for NISQ devices.

## Key findings

- Successfully simulated a two-level system with amplitude damping.
- Demonstrated simulation of a dissipative transverse field Ising model.
- Achieved short-time evolution with reduced circuit depth.

## Abstract

Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits makes the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of UQA via NISQ technology. Based on this framework, we present two quantum-assisted quantum algorithms for simulating open quantum systems, which utilize two parameterized quantum circuits to achieve a short-time evolution. We propose a variational quantum state preparation method, as a subroutine to prepare the ancillary state, for loading a classical vector into a quantum state with a shallow quantum circuit and logarithmic number of qubits. We demonstrate numerically our approaches for a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model on two sites.