Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

Abstract

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

arXiv comment6 pages, 5 figures (+ 5 pages, 7 figures)

References in corpus (76)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Electronic transport in two dimensional graphene
• The density-matrix renormalization group
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Average Entropy of a Subsystem
• Continuous-time Monte Carlo methods for quantum impurity models
• Characterizing Quantum Supremacy in Near-Term Devices
• The Kernel Polynomial Method
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Scalable Quantum Simulation of Molecular Energies
• Nonequilibrium dynamical mean-field theory and its applications
• Canonical Typicality
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Optimal Quantum Circuits for General Two-Qubit Gates
• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Simulating Physical Phenomena by Quantum Networks
• Quantum Metropolis Sampling
• Spin diffusion from an inhomogeneous quench in an integrable system
• The Ergodic Side of the Many-Body Localization Transition
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Simulating quantum many-body dynamics on a current digital quantum computer
• Typicality for Generalized Microcanonical Ensembles
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Canonical Thermal Pure Quantum State
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• The problem of equilibration and the computation of correlation functions on a quantum computer
• Dynamical typicality of quantum expectation values
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Quantum localization bounds Trotter errors in digital quantum simulation
• 16-qubit IBM universal quantum computer can be fully entangled
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Simulation of Nonequilibrium Dynamics on a Quantum Computer
• Spin-current autocorrelations from single pure-state propagation
• Efficient Generation of Generic Entanglement
• Spin decay and quantum parallelism
• Quantum hardware simulating four-dimensional inelastic neutron scattering
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Algorithms for quantum simulation at finite energies
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• Regression relation for pure quantum states and its implications for efficient computing
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Efficient Quantum Algorithm for Computing n-time Correlation Functions
• Quantum computation of magnon spectra
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Random State Technology
• Quantum parallelism as a tool for ensemble spin dynamics calculations
• Scaling of diffusion constants in the spin-1/2 XX ladder
• Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit
• Optimal two-qubit gate for generation of random bipartite entanglement
• Parameters of Pseudo-Random Quantum Circuits
• Dynamical structure factors of dynamical quantum simulators
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Quantifying the sensitivity to errors in analog quantum simulation
• Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation
• Dissipation-assisted operator evolution method for capturing hydrodynamic transport

Cited by in corpus (35)

• Strong quantum computational advantage using a superconducting quantum processor
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• First-Order Trotter Error from a Second-Order Perspective
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Transport and entanglement growth in long-range random Clifford circuits
• Optimal compression of quantum many-body time evolution operators into brickwall circuits
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Quantum criticality using a superconducting quantum processor
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Many-body delocalization from embedded thermal inclusion
• Certification of quantum states with hidden structure of their bitstrings
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• Probing spin hydrodynamics on a superconducting quantum simulator
• Deep thermalization under charge-conserving quantum dynamics
• Success of digital adiabatic simulation with large Trotter step
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• Quantum dynamics of disordered arrays of interacting superconducting qubits: signatures of quantum collective states
• Quantum simulation using noisy unitary circuits and measurements
• Calculating the many-body density of states on a digital quantum computer
• Lower Bounds for the Trotter Error
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
• Non-Randomness of Google's Quantum Supremacy Benchmark
• Dynamical chaos in the integrable Toda chain induced by time discretization
• High-fidelity dimer excitations using quantum hardware
• Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium
• Engineering Hierarchical Symmetries
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Anomalous transport in U(1)-symmetric quantum circuits
• Trotter transition in BCS pairing dynamics