Quantum algorithm to simulate Lindblad master equations

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 d...

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Main Authors: Evan Borras, Milad Marvian
Format: Article
Language:English
Published: American Physical Society 2025-04-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.7.023076
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author Evan Borras
Milad Marvian
author_facet Evan Borras
Milad Marvian
author_sort Evan Borras
collection DOAJ
description 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.
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spelling doaj-art-a43604972bcd44eeaacba53c5c2f56582025-08-20T02:24:31ZengAmerican Physical SocietyPhysical Review Research2643-15642025-04-017202307610.1103/PhysRevResearch.7.023076Quantum algorithm to simulate Lindblad master equationsEvan BorrasMilad MarvianWe 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.http://doi.org/10.1103/PhysRevResearch.7.023076
spellingShingle Evan Borras
Milad Marvian
Quantum algorithm to simulate Lindblad master equations
Physical Review Research
title Quantum algorithm to simulate Lindblad master equations
title_full Quantum algorithm to simulate Lindblad master equations
title_fullStr Quantum algorithm to simulate Lindblad master equations
title_full_unstemmed Quantum algorithm to simulate Lindblad master equations
title_short Quantum algorithm to simulate Lindblad master equations
title_sort quantum algorithm to simulate lindblad master equations
url http://doi.org/10.1103/PhysRevResearch.7.023076
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AT miladmarvian quantumalgorithmtosimulatelindbladmasterequations