Preconditioned quantum linear system algorithm

TL;DR

This paper introduces a generalized quantum linear system algorithm with a state preparation routine and quantum-compatible preconditioner, enabling exponential speedups in solving linear systems and computing electromagnetic scattering cross sections.

Contribution

It presents a novel quantum algorithm that extends previous methods to more general problems using a new preconditioning technique and state preparation routine.

Findings

Enables exponential speedup over classical solvers for certain linear systems

Demonstrates application to electromagnetic scattering cross section calculation

Integrates a quantum-compatible preconditioner to broaden problem applicability

Abstract

We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.