Benchmarking Quantum Simulators using Ergodic Quantum Dynamics

Abstract

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated spatiotemporal control. Our approach utilizes newly discovered universal fluctuations emerging from generic Hamiltonian dynamics, and it does not require any fine-tuned control over state preparation, quantum evolution, or readout capability. It only needs a small number of experimental measurements, achieving near optimal sample complexity: in ideal cases, a percent-level precision is obtained with $\sim 10^3$ measurements independent of system size. Furthermore, the accuracy of our fidelity estimation improves with increasing system size. We numerically demonstrate our protocol for a variety of quantum simulator platforms such as itinerant particles on optical lattices, trapped ions, and Rydberg atoms. We discuss further applications of our method for advanced tasks such as multi-parameter estimation of quantum states and processes.

7+27 pages, 3+9 figures v2: version accepted in Physical Review Letters

References in corpus (13)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum trajectories and open many-body quantum systems
• Efficient quantum state tomography
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Direct Fidelity Estimation from Few Pauli Measurements
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Evenly distributed unitaries: on the structure of unitary designs
• The randomized measurement toolbox
• Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
• Measurements conspire nonlocally to restructure critical quantum states
• Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice

Cited by in corpus (26)

• Phase transition in Random Circuit Sampling
• Benchmarking highly entangled states on a 60-atom analog quantum simulator
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Bell sampling from quantum circuits
• Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• Volume-entangled exact scar states in the PXP and related models in any dimension
• Anticoncentration and state design of random tensor networks
• Efficient Local Classical Shadow Tomography with Number Conservation
• Optimized trajectory unraveling for classical simulation of noisy quantum dynamics
• Quantifying Quantum Computational Advantage on a Processor of Ultracold Atoms
• The power and limitations of learning quantum dynamics incoherently
• Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Concentration of quantum equilibration and an estimate of the recurrence time
• How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos
• Accreditation of Analogue Quantum Simulators
• Projected ensemble in a system with conserved charges with local support
• A protocol to characterize errors in quantum simulation of many-body physics
• Fast nuclear-spin entangling gates compatible with large-scale atomic arrays
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Partial projected ensembles and spatiotemporal structure of information scrambling
• On Computational Complexity of Unitary and State Design Properties
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Characterization of the chaotic phase in the tilted Bose-Hubbard model
• Rationally independent free fermions with local hopping