Quantum Simulation of Nonlinear Classical and Semiclassical Dynamics
Ilon Joseph (Lawrence Livermore National Laboratory)
Friday 23 July 2021
at 17:00 Lisbon time
In principle, future error-corrected quantum computers promise to accelerate the solution of many numerical algorithms that are important for scientific computing. If the system is Hamiltonian, then one natural approach is to simulate a quantized version of the system. Another natural approach is to reformulate the conservation of probability, the Liouville equation, as an equivalent Schrodinger equation with Hermitian Hamiltonian and a unitary evolution operator. The introduction of a complex phase factor allows one to represent semiclassical dynamics through a configuration space version of the Koopman-van Hove (KvH) equation, intimately related to the phase space KvH equation introduced in Ref. . This semiclassical KvH formulation also solves the important problem of self-consistently coupling classical and quantum systems together. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of the unitary evolution operator. Using this approach to quantum simulation is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Hamiltonian is sparse . Using amplitude estimation for the calculation of observables and quantum walk techniques for state preparation can lead to up to a quadratic improvement over probabilistic Monte Carlo algorithms .
Work performed by LLNL under US DOE contract DE-AC52-07NA27344 was supported by the DOE Fusion Energy Sciences project “Quantum Leap for FES,” SCW-1680 and by LLNL Laboratory Directed Research and Development project 19-FS-072.
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