Quantum algorithm to simulate Lindblad master equations

Borras, Evan; Marvian, Milad

doi:10.1103/PhysRevResearch.7.023076

Quantum algorithm to simulate Lindblad master equations

Journal Article · Tue Apr 22 00:00:00 EDT 2025 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.7.023076· OSTI ID:2561468

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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 family of Markovian master equations it can be applied to, 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.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024685

OSTI ID:: 2561468

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 7; ISSN 2643-1564; ISSN PPRHAI

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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