Variational quantum algorithm for nonequilibrium steady states

Nobuyuki Yoshioka,Keisuke Fujii,Yuya O. Nakagawa,Kosuke Mitarai

doi:10.1103/physrevresearch.2.043289

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.

Highlights

Technological developments in quantum devices have reached a stage to realize the near-term quantum computers that contain from tens to hundreds of qubits with high gate fidelity, their qubits are prone to error [1,2,3]
The cost function L†Lis evaluated via sampling each Pauli term from noisy quantum circuit, whose variational parameters are optimized by the sequential minimal optimization technique [49]
We have proposed the variational quantum algorithm to obtain the nonequilibrium steady state (NESS) of an open quantum many-body system, named the dissipative-system variational quantum eigensolver

Summary

Introduction

Technological developments in quantum devices have reached a stage to realize the near-term quantum computers that contain from tens to hundreds of qubits with high gate fidelity, their qubits are prone to error (or not faulttolerant) [1,2,3] Such quantum computers are dubbed as the noisy intermediate-scale quantum (NISQ) devices [4]. Proposed for obtaining the ground state and its energy of a given Hamiltonian, the extensions of the VQE scheme are capable of the excited states and their energies [16,17,18,19,20,21] Such developments including actual quantum simulations [22,23,24,25] focus only on closed quantum systems, which is a system that does not exchange energy with its external environment.

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Conclusion