Random State Technology

TL;DR

This paper reviews and extends the mathematical foundations of random state-based numerical simulation methods, demonstrating their versatility in physics, quantum computing, and information theory.

Contribution

It provides a comprehensive, self-contained extension of the mathematical basis for random state technology and explores new applications in quantum supremacy and information theory.

Findings

Effective calculation of physical properties using random states

Application of random state methods to quantum supremacy experiments

Utility of random state concepts in quantum information theory

Abstract

We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations of physically relevant properties such as the density of states of large single particle systems, the specific heat, current-current correlations, density-density correlations, and electron spin resonance spectra of many-body systems. We explore a new field of applications of the random state technology by showing that it can be used to analyze numerical simulations and experiments that aim to realize quantum supremacy on a noisy intermediate-scale quantum processor. Additionally, we show that concepts of the random state technology prove useful in quantum information theory.