Quantum Simulation of Open Quantum Systems Using Density-Matrix Purification

TL;DR

This paper introduces a novel framework for simulating open quantum systems on quantum computers by transforming the density matrix into a wavefunction, enabling unitary evolution of non-unitary dynamics with fewer qubits.

Contribution

The authors present a density-matrix purification method that reduces qubit requirements and allows simulation of open quantum system dynamics on quantum hardware.

Findings

Method successfully simulates open system dynamics on quantum devices.

Results agree with classical calculations for two-level and two-site models.

Demonstrates feasibility of non-unitary operations on NISQ devices.

Abstract

Electronic structure and transport in realistically-sized systems often require an open quantum system (OQS) treatment, where the system is defined in the context of an environment. As OQS evolution is non-unitary, implementation on quantum computers -- limited to unitary operations -- is challenging. We present a general framework for OQSs where the system's $d \times d$ density matrix is recast as a $d^{2}$ wavefunction which can be evolved by unitary transformations. This theory has two significant advantages over conventional approaches: (i) the wavefunction requires only an $n$-qubit, compared to $2n$-qubit, bath for an $n$-qubit system and (ii) the purification includes dynamics of any pure-state universe. We demonstrate this method on a two-level system in a zero temperature amplitude damping channel and a two-site quantum Ising model. Quantum simulation and experimental-device results agree with classical calculations, showing promise in simulating non-unitary operations on NISQ quantum devices.