Applied Math And Analysis Seminar
Tuesday, March 23, 2021, 3:15pm, Virtual
Dong An (University of California, Berkeley, Mathematics)
Adiabatic and preconditioned quantum linear system solvers

Abstract:

As Google declared that "quantum supremacy" was reached in 2019, there has been rapidly increasing interest in designing efficient algorithms which are suitable on quantum computers and can solve problems infeasible for classical computers. In this talk, we will discuss two quantum algorithms to solve linear systems of equations, namely $Ax=b$, and the underlying mathematical foundation. The first algorithm is based on adiabatic quantum computing (AQC) with an optimally tuned scheduling function, which can readily solve a quantum linear system problem (QLSP) with cost near optimal in both condition number and target accuracy. To further reduce the cost for ill-conditioned systems, we will introduce a second quantum algorithm based on fast inversion, which can be used as a preconditioner for solving linear systems. No prior knowledge on quantum computation is necessary.

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