Probing many-body localization crossover in quasiperiodic Floquet circuits on a quantum processor

Abstract

Many-body localization (MBL) provides a mechanism by which interacting quantum systems evade thermalization, leading to persistent memory of initial conditions and slow entanglement growth. Probing these dynamical signatures in large systems and at long evolution times remains challenging for both classical simulations and current quantum devices. Here we experimentally investigate the ergodic-MBL crossover in quasiperiodic Floquet Ising systems using up to 144 qubits on an IBM Quantum processor. By implementing deep Floquet circuits reaching up to 5000 cycles, we access long-time many-body dynamics beyond the regime explored in previous quantum computing experiments. Measurements of autocorrelation functions reveal a smooth crossover from rapid thermalization at weak quasiperiodic potential strength to persistent correlations in the strong-disorder regime. Notably, in addition to the one-dimensional system, we also observe clear signatures consistent with localization behavior in the two-dimensional system. Furthermore, the quantum Fisher information exhibits logarithmic growth over thousands of Floquet cycles, providing evidence for slow entanglement spreading characteristic of the MBL regime. These results demonstrate that programmable quantum processors can serve as experimental platforms for probing nonergodic quantum many-body dynamics and exploring localization phenomena in regimes beyond the reach of classical simulations.

Figures (4)

• Figure 1: Kicked Ising systems subjected to quasiperiodic (QP) potentials. a Circuit representation of the one-dimensional kicked Ising Floquet operator ${\hat{U}}_{\rm F}^{(1)}$. A QP potential with strength $W$ is applied through the layer of RZ gates, which induces localization in the Hilbert space of qubits. The Ising coupling is decomposed in two layers of RZZ gates (red and blue), followed by a global RX rotation. The boxed block indicates a single Floquet cycle, which is repeated $t$ times. b Schematic illustration of the two-dimensional kicked Ising model with QP potentials. The Floquet circuit acts on a heavy-hexagonal lattice and includes red, blue, and green coupling layers. A QP potential is applied along $L^{\rm R/G/B}_{m}$ ($m = 0, 1, 2, \cdots$), indicated by colored stripes (red, green, or blue) passing through the qubits and forming one-dimensional paths. Each hexagon in the lattice therefore contains three different stripe directions. c Part of the two-dimensional Floquet circuit ${\hat{U}}_{\rm F}^{(2)}$ acting on a single hexagonal unit. The RZ and RZZ gates are arranged in three colored layers.
• Figure 2: Autocorrelation function in the one-dimensional quasiperiodic (QP) kicked Ising model. a Connectivity layout of qubits on the ibm_kobe processor. White circles highlight the 129 qubits selected for our experiments, forming a one-dimensional chain. Colored bonds represent nearest-neighbour RZZ couplings. Red (blue) bonds indicate the even (odd) layer of parallelized RZZ gates (see also Fig. \ref{['fig1']}a). b Experimental results obtained using fractional gates up to 100 Floquet cycles. Symbol colors indicate the strength of $W$. Error bars are estimated from the average measurement errors of ${\hat{Z}}_j$, but are sufficiently small to be negligible. For comparison, tDMRG results are shown as solid lines with the corresponding colors, up to the Floquet cycle $t$ for which convergence is confirmed with bond dimension $\chi=512$ (indicated by vertical dotted lines). c Same as b but without fractional gates. d Longer-time evolution of the autocorrelation up to $3000$ Floquet cycles using fractional gates. The dashed line shows a power-law fit to the data with $W < 4.0$.
• Figure 3: Autocorrelation function in the two-dimensional quasiperiodic (QP) kicked Ising model. a Connectivity layout for the 28-qubit system in two dimensions. b Measured autocorrelation function $A(t)$ for the 28-qubit system for $t \leq 100$. Symbol colors indicate different values of $W$. Solid lines show the corresponding state-vector simulation results. c Left: long-time evolution of the 28-qubit system up to 5000 Floquet cycles. Right: corresponding state-vector simulation results. The inset extends the experimental data in b to longer times up to 5000 Floquet cycles. Symbol colors correspond to those in b. d Same as a but for the 144-qubit system. e Same as b but for the 144-qubit system. f Long-time evolution of the 144-qubit system up to 5000 Floquet cycles. The dashed line shows a power-law fit to the data with $W < 4$.
• Figure 4: Time evolution of the quantum Fisher information (QFI).a Measured QFI for the one-dimensional kicked Ising model with 129 qubits. For $W \lesssim 3.0$, the QFI rapidly approaches the Haar random value $F_{Q}^{\rm Haar} \approx 4/N$, indicated by the dashed black line. For $W \gtrsim 3.5$, the spreading of correlations is suppressed, leading to logarithmic growth characteristic to the MBL regime. The QFI is evaluated from $2^{14}=16384$ measurement shots. Error bars are obtained using the bootstrap method applied to the measured bitstrings. b Numerical fit of the one-dimensional results in the MBL regime. The data are well described by a logarithmic function $a + b \ln t$. c Same as a but for the two-dimensional kicked Ising model with 144 qubits. d Same as b but for the two-dimensional case. Logarithmic growth is observed for $W \gtrsim 4$, whereas for smaller $W$ the QFI approaches the Haar random value.