Simulating Floquet scrambling circuits on trapped-ion quantum computers

Abstract

Complex quantum many-body dynamics spread initially localized quantum information across the entire system. Information scrambling refers to such a process, whose simulation is one of the promising applications of quantum computing. We demonstrate the Hayden-Preskill recovery protocol and the interferometric protocol for calculating out-of-time-ordered correlators to study the scrambling property of a one-dimensional kicked-Ising model on 20-qubit trapped-ion quantum processors. The simulated quantum circuits have a geometrically local structure that exhibits the ballistic growth of entanglement, resulting in the circuit depth being linear in the number of qubits for the entire state to be scrambled. We experimentally confirm the growth of signals in the Hayden-Preskill recovery protocol and the decay of out-of-time-ordered correlators at late times. As an application of the created scrambling circuits, we also experimentally demonstrate the calculation of the microcanonical expectation values of local operators adopting the idea of thermal pure quantum states. Our experiments are made possible by extensively utilizing one of the highest-fidelity quantum processors currently available and, thus, should be considered as a benchmark for the current status of the most advanced quantum computers.

30 pages, 17 figures, accepted version

References in corpus (24)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Black holes as mirrors: quantum information in random subsystems
• Dynamics of Loschmidt echoes and fidelity decay
• Equilibrium states of generic quantum systems subject to periodic driving
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Semiclassical Foundation of Universality in Quantum Chaos
• Loschmidt Echo
• Preparing random states and benchmarking with many-body quantum chaos
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Random phase vector for calculating the trace of a large matrix
• Chaos and Complexity of quantum motion
• Re-examining the quantum volume test: Ideal distributions, compiler optimizations, confidence intervals, and scalable resource estimations
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
• Sachdev-Ye-Kitaev model on a noisy quantum computer
• Designs via Free Probability
• Classical algorithms for many-body quantum systems at finite energies
• Towards Quantum Gravity in the Lab on Quantum Processors
• Large-scale simulations of Floquet physics on near-term quantum computers
• Energy-filtered random-phase states as microcanonical thermal pure quantum states
• Calculating the many-body density of states on a digital quantum computer
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers
• Evaluating thermal expectation values by almost ideal sampling with Trotter gates

Cited by in corpus (4)

• Computing n-time correlation functions without ancilla qubits
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer