Random State Technology

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.

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Cited by in corpus (40)

• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Diffusion constants from the recursion method
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Probing spin hydrodynamics on a superconducting quantum simulator
• Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3
• Purity of thermal mixed quantum states
• Quantum simulation using noisy unitary circuits and measurements
• Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
• Energy-filtered random-phase states as microcanonical thermal pure quantum states
• Calculating the many-body density of states on a digital quantum computer
• Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-Classical Solutions
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Porter-Thomas fluctuations in complex quantum systems
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• A Time-Dependent Random State Approach for Large-scale Density Functional Calculations
• Signatures of the finite-temperature mirror symmetry breaking in the $S$=1/2 Shastry-Sutherland model
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Nontrivial damping of quantum many-body dynamics
• A spectrum adaptive kernel polynomial method
• Quantum process tomography of continuous-variable gates using coherent states
• Understanding the physics of D-Wave annealers: From Schrödinger to Lindblad to Markovian Dynamics
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Evaluating thermal expectation values by almost ideal sampling with Trotter gates
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• On the fragility of gate-error metrics in simulation models of flux-tunable transmon quantum computers
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Sample complexity of matrix product states at finite temperature
• Faster randomized partial trace estimation
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Nontrivial damping of magnetization currents in perturbed spin chains