Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

Journal Article · Thu Jan 01 00:00:00 EST 2026 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-025-05509-w· OSTI ID:3012839

An, Dong; Childs, Andrew M; Lin, Lin

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 3012839
• Journal Information: Communications in Mathematical Physics, Journal Name: Communications in Mathematical Physics Journal Issue: 1 Vol. 407
• Country of Publication: United States
• Language: English