Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters
Dong An, Andrew M. Childs, Lin Lin
Abstract
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.
Topics & Concepts
Unitary stateHamiltonian (control theory)MathematicsQuantumLinear scaleScalingQuantum algorithm for linear systems of equationsQuantum algorithmApplied mathematicsQuantum phase estimation algorithmDifferential evolutionQuantum systemTime evolutionStatistical physicsUnitary matrixLinear systemState-transition matrixHamiltonian systemNonlinear systemMatrix (chemical analysis)Quantum dynamicsQuantum computerLinear differential equationDifferential equationPhysical systemExponential growthAlgorithmQuantum operationLinear mapHamiltonian matrixQuantum stateUnitary operatorState (computer science)Hamiltonian mechanicsQuantum Computing Algorithms and ArchitectureQuantum many-body systemsSpectroscopy and Quantum Chemical Studies