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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| Format: | Article |
| Language: | English |
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American Physical Society
2025-04-01
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| 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. |
| format | Article |
| id | doaj-art-a43604972bcd44eeaacba53c5c2f5658 |
| institution | OA Journals |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| 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 |
| work_keys_str_mv | AT evanborras quantumalgorithmtosimulatelindbladmasterequations AT miladmarvian quantumalgorithmtosimulatelindbladmasterequations |