Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters
Abstract 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.
Authors
- Andrew M. Childs (ORCID: https://orcid.org/0000-0002-9903-837X)
- Dong An (ORCID: https://orcid.org/0000-0002-2964-3603)
- Lin Lin (ORCID: https://orcid.org/0000-0001-6860-9566)
Institutions
- QB3 (US)
- Lawrence Berkeley National Laboratory (US)
- Joint Center for Quantum Information and Computer Science (US)
- University of Maryland, College Park (US)
- University of California, Berkeley (US)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2025-12-08
- DOI
- https://doi.org/10.1007/s00220-025-05509-w
- Citations
- 3
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 7.44
Funders
- National Science Foundation
- U.S. Department of Defense
- U.S. Department of Energy
- Office of Science
- Advanced Scientific Computing Research