Digital quantum simulation of many-body localization crossover in a disordered kicked Ising model

TL;DR

This paper addresses the challenge of simulating nonequilibrium dynamics and the many-body localization (MBL) crossover in Floquet quantum many-body systems on near-term quantum devices. It demonstrates a digital quantum simulation of the disordered kicked Ising model on a heavy-hex IBM device using $U_{ m F}=e^{-rac{i}{2}H_Z T}e^{-rac{i}{2}H_X T}$ and a 10-step Trotterized evolution, probing scrambling and localization via out-of-time-ordered correlators (OTOCs). The authors introduce the effective quantum volume and employ two error-mitigation methods—operator renormalization and zero-noise extrapolation—to validate the results, locating a crossover at $W_c\approx 0.18$ between chaotic and MBL regimes. They demonstrate the feasibility of studying nonequilibrium Floquet dynamics with dozens of qubits on current devices, suggesting a viable path toward larger-scale quantum simulations ahead of fault-tolerant quantum computing.

Abstract

Simulating nonequilibrium dynamics of quantum many-body systems is one of the most promising applications of quantum computers. However, a faithful digital quantum simulation of the Hamiltonian evolution is very challenging in the present noisy quantum devices. Instead, nonequilibrium dynamics under the Floquet evolution realized by the Trotter decomposition of the Hamiltonian evolution with a large Trotter step size is considered to be a suitable problem for simulating in the present or near-term quantum devices. In this work, we propose simulating the many-body localization crossover as such a nonequilibrium problem in the disordered Floquet many-body systems. As a demonstration, we simulate the many-body localization crossover in a disordered kicked Ising model on a heavy-hex lattice using $60$ qubits from $156$ qubits available in the IBM Heron r2 superconducting qubit device named ibm\_fez. We compute out-of-time-ordered correlators as an indicator of the many-body localization crossover. From the late-time behavior of out-of-time-ordered correlators, we locate the quantum chaotic and many-body localized regimes as a function of the disorder strength. The validity of the results is confirmed by comparing two independent error mitigation methods, that is, the operator renormalization method and zero-noise extrapolation.

Figures (8)

• Figure 1: Layout of qubits in ibm_fez. The vertices colored in dark blue and red denote the qubits used in our experiments. The vertex colored in red denotes the position of the butterfly operator. The edges denote the connectivity of qubits in IBM's Heron r2 devices.
• Figure 2: Disorder and site average of the normalized OTOCs defined in Eq. \ref{['eq:normalized_OTOC']} as a function of the number of the Trotter steps. Inset qubit layouts show the positions of $Z_m$, which are colored in green, and $x$ is the distance of the $m$th qubit measured from the qubit that the butterfly operator $X_1$ acts on. The average of the normalized OTOCs over $m$ with the same distance $x$ is taken simultaneously with the disorder average.
• Figure 3: Disorder and site average of the normalized OTOCs defined in Eq. \ref{['eq:normalized_OTOC']} as functions of the distance of the measured qubits $Z_m$ from the butterfly operator $X_1$$x$.
• Figure 4: Disorder and site average of the normalized OTOCs defined in Eq. \ref{['eq:normalized_OTOC']} as functions of (a) the disorder strength $W$ and (b) the distance $x$ of the measured qubits $Z_m$ from the butterfly operator $X_1$.
• Figure 5: Disorder and site average of the effective quantum volume defined in Eq. \ref{['eq:quantum_volume']} as a function of the number of the Trotter steps. Inset qubit layouts show the positions of $Z_m$, which are colored in green, and $x$ is the distance of the $m$th qubit measured from the qubit that the butterfly operator $X_1$ acts on. The average of the effective quantum volume over $m$ with the same distance $x$ is taken simultaneously with the disorder average.