Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark

TL;DR

This paper introduces a quantum benchmark called the quantum LINPACK benchmark, utilizing a new input model called RACBEM, to evaluate quantum computers' performance on linear algebra tasks relevant to scientific computing.

Contribution

The paper proposes the RACBEM model for efficient quantum implementation and introduces the quantum LINPACK benchmark to assess quantum computer performance on linear algebra problems.

Findings

Demonstrated implementation of linear algebra operations on IBM Q devices.

Showed RACBEM's adaptability to various quantum architectures.

Validated the benchmark's relevance for scientific computing tasks.

Abstract

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the RAndom Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer, and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.