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DOE OSTI · 3012839

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

An, Dong [Univ. of Maryland, College Park, MD (United States)] (ORCID:0000000229643603)·Childs, Andrew M. [Univ. of Maryland, College Park, MD (United States)]·Lin, Lin [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000168609566)
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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.

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Applied Dynamical SystemsCalculus of Variations and OptimizationDifferential EquationsLinear AlgebraOrdinary Differential EquationsQuantum Dynamics and Differential Equation TechniquesQuantum Simulations

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An, Dong [Univ. of Maryland, College Park, MD (United States)] (ORCID:0000000229643603), Childs, Andrew M. [Univ. of Maryland, College Park, MD (United States)], Lin, Lin [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000168609566). 2025-12-08. Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters. https://doi.org/10.1007/s00220-025-05509-w

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