Driven-dissipative quantum mechanics on a lattice: Simulating a fermionic reservoir on a quantum computer

TL;DR

This paper presents quantum algorithms for simulating driven-dissipative fermionic lattice systems, demonstrating their implementation on IBM quantum hardware and paving the way for studying complex non-equilibrium quantum phenomena.

Contribution

It introduces two quantum circuits for simulating non-interacting driven-dissipative electrons, including a steady-state preparation method, on a quantum computer.

Findings

Successfully simulated up to 5 Trotter steps on IBM quantum hardware.

Demonstrated dissipative state preparation in a single quantum circuit.

Methods can be extended to interacting systems and longer simulation times.

Abstract

The driven-dissipative many-body problem remains one of the most challenging unsolved problems in quantum mechanics. The advent of quantum computers may provide a unique platform for efficiently simulating such driven-dissipative systems. But there are many choices for how one can engineer the reservoir. One can simply employ ancilla qubits to act as a reservoir and then digitally simulate them via algorithmic cooling. A more attractive approach, which allows one to simulate an infinite reservoir, is to integrate out the bath degrees of freedom and describe the driven-dissipative system via a master equation, that can also be simulated on a quantum computer. In this work, we consider the particular case of non-interacting electrons on a lattice driven by an electric field and coupled to a fermionic thermostat. Then, we provide two different quantum circuits: the first one reconstructs the full dynamics of the system using Trotter steps, while the second one dissipatively prepares the final non-equilibrium steady state in a single step. We run both circuits on the IBM quantum experience. For circuit (i), we achieved up to 5 Trotter steps. When partial resets become available on quantum computers, we expect that the maximum simulation time can be significantly increased. The methods developed here suggest generalizations that can be applied to simulating interacting driven-dissipative systems.