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From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping
Hsuan-Cheng Wu, Xiantao Li
Nonlinear stochastic differential equations (SDEs) underlie molecular modeling and drug discovery, quantitative finance, stochastic learning, and uncertainty quantification. Their…
Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation
Xiantao Li
We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC), viewed as imaginary-time projection for ground-state calculation as an ensemble of one-body…
From Linear Differential Equations to Unitaries: A Moment-Matching Dilation Framework with Near-Optimal Quantum Algorithms
Xiantao Li
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-uni…
Structure-preserving quantum algorithms for linear and nonlinear Hamiltonian systems
Hsuan-Cheng Wu, Xiantao Li
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustnes…