Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems

TL;DR

This paper introduces a low-rank variational quantum algorithm designed to efficiently simulate the real-time dynamics of open quantum systems governed by the Lindblad equation, using fewer quantum resources by exploiting low-rank density matrices.

Contribution

It develops a novel variational quantum algorithm that encodes the density matrix with low-rank assumptions, reducing qubit requirements for simulating open quantum system dynamics.

Findings

Efficient simulation of a 2D dissipative transverse field Ising model.

Algorithm requires fewer qubits than full density matrix encoding.

Effective in low-rank regime with limited quantum resources.

Abstract

The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational Ans\"atze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.