Variational Quantum Algorithm for Non-equilibrium Steady States

TL;DR

This paper introduces a hybrid quantum-classical algorithm, dVQE, to simulate non-equilibrium steady states in open quantum systems, combining variational techniques with quantum circuit design for efficient computation.

Contribution

It presents a novel variational algorithm that maps mixed states to pure states for simulating steady states of open quantum systems using quantum circuits.

Findings

Successfully demonstrated on classical and quantum hardware

Efficiently computes physical observables in open quantum systems

Provides a scalable approach for non-equilibrium steady state simulation

Abstract

We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits and design the unitary quantum circuit to fulfill the requirements for a density matrix. This allows us to define a cost function that consists of the time evolution generator of the quantum master equation. Evaluation of physical observables is, in turn, carried out by a quantum circuit with the original number of qubits. We demonstrate our dVQE scheme by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti Quantum Cloud Service.