Random State Technology

2020/10/09 by Fengpin Jin, Fengping Jin, Dennis Willsch +4
Computer Science · Physics and Astronomy · #Computer simulation #Field (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems #Quantum state #Random field #Random variable #Spin (aerodynamics) #State (computer science) #Stochastic process #physics.comp-ph #quant-ph

paper · pdf · doi:10.7566/jpsj.90.012001

published as J. Phys. Soc. Jpn., Vol.90, No.1, Article ID: 012001 (2021)

arxiv created 2020/10/09 · openalex created_date 2020/10/15 · openalex publication_date 2020/12/04 · arxiv updated 2020/12/07 · openalex updated_date 2026/08/05

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.

Citations

• Direct dialling of Haar random unitary matrices
• Fidelity for Mixed Quantum States
• Giant enhancement of quantum decoherence by frustrated environments
• Approach to thermal equilibrium of macroscopic quantum systems
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
• Distance measures to compare real and ideal quantum processes
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Chaos and Quantum Thermalization
• The Kernel Polynomial Method
• Random matrix theory
• Random phase vector for calculating the trace of a large matrix
• Quantum statistical mechanics in a closed system
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Decoherence by a spin thermal bath: Role of the spin-spin interactions
• Fast algorithm for finding the eigenvalue distribution of very large matrices
• Origin of the Canonical Ensemble: Thermalization with Decoherence
• Scalable noise estimation with random unitary operators
• Characterizing quantum supremacy in near-term devices
• Quantum Computing in the NISQ era and beyond
• Canonical thermalization
• Characteristic Vectors of Bordered Matrices With Infinite Dimensions