A quantum algorithm to simulate Lindblad master equations

TL;DR

This paper introduces a quantum algorithm for simulating Lindblad master equations efficiently, reducing complexity and eliminating the need for ancillary qubits, with extensions to time-dependent cases and broader applications.

Contribution

The authors develop a novel quantum simulation algorithm for Lindblad equations using a second-order product formula, simplifying implementation and extending to non-Markovian dynamics.

Findings

Eliminates ancillary qubits for dissipation simulation

Reduces gate complexity related to jump operators

Provides a new error bound for time-dependent Liouvillians

Abstract

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the noise model when there is access to limited ancillary systems, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest.