Explicit near-optimal quantum algorithm for solving the advection-diffusion equation
ORAL
Abstract
Quantum computing has the potential to speed up simulations of classical dynamics by leveraging quantum superposition and entanglement to parallelize the processing of high-dimensional data. Yet, due to the intrinsically unitary nature of quantum mechanics, modeling dissipative dynamics has required significant development. Quantum algorithms for dissipative dynamics are usually based on the transformation of nonunitary initial-value problems into a system of linear equations which then can be solved by a quantum linear system algorithm such as the quantum singular value transformation. However, to reduce the number of calls to the initialization oracle, it is better to use the Linear Combination of Hamiltonian Simulations (LCHS) algorithm. We propose an explicit LCHS quantum circuit, explain how to achieve high success probability and an optimal linear scaling with time for this method, and test it on modeling the advection-diffusion equation on a classical emulator of fault-tolerant quantum computers.
*This work was supported by the U.S. Department of Energy (DOE) Office of Fusion Energy Sciences “Quantum Leap for Fusion Energy Sciences” Project No. FWP-SCW1680 at Lawrence Livermore National Laboratory (LLNL). Work was performed under the auspices of the U.S. DOE under LLNL Contract DE-AC52–07NA27344.This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC award FES-ERCAP0028618.
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Presenters
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Ivan Novikau
- Lawrence Livermore National Laboratory (LLNL)