Observation of Thermalization and Information Scrambling in a Superconducting Quantum Processor

Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the $XX$-ladder model and the one-dimensional $XX$ model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the $XX$ ladder. In contrast, we show that the $XX$ chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.

Figure 1

Superconducting quantum circuit and experimental pulse sequences. (a) False-color optical micrograph of the superconducting circuit. Each qubit has an independent control line for the $XY$ and $Z$ control (the yellow region), coupled to a separate readout resonator (the purple region). (b) A schematic graph of the superconducting quantum circuit. The up and down arrows indicate that the initial state of the qubit is $|1⟩$ and $|0⟩$, respectively. The qubits $Q_1–Q_{12}$ are employed in the quantum simulation of $XX$ chain. The qubits $Q_1–Q_6$ and $Q_{13}–Q_{18}$ are employed in the quantum simulation of $XX$ ladder. (c),(d) The experimental pulse sequence of the quantum simulation of $XX$ chain and ladder, respectively. The pulse sequences consist of initialization, evolution, and readout. In the initialization, all qubits are at $|0⟩$, and the $X$ gates are applied on the qubits whose chosen initial state is $|1⟩$. Next, the qubits are tuned to the working point via $Z$ pulses, and the time evolution is realized. Finally, the measurements are performed after tuning the qubits back to their idle points.

Figure 2

Dynamics of local densities and the operator distances. (a) Experimental data of the time evolution of local observables $n_{|1⟩}(t)$ in the qubit chain and ladder. Panel (b) is similar to (a), but for the local observable $n_{|0⟩}(t)$. (c) The time evolution of the operator distance between the quenched and thermal states in the chain and ladder. The solid lines are numerics without considering decoherence. The error bars of experimental data are smaller than the size of symbols and not shown here (see Ref. [29] for the values of errors of all experimental data).

Figure 3

Dynamics of entanglement entropy with different subsystem length $l$. (a) Time evolution of EE in the qubit chain with the subsystem consisting of $Q_1$ and $Q_2$. (b) Time evolution of EE in the qubit ladder with the subsystem consisting of $Q_1$ and $Q_2$. Panels (c) and (d) are similar to (a) and (b), respectively, but with the subsystem consisting of $Q_1–Q_4$. Panels (e) and (f) are similar to (a) and (b), respectively, but with the subsystem consisting of $Q_1–Q_6$. (g) The time-averaged EE as a function of $l$. The solid lines in (a) to (f) are numerics without considering decoherence. The dashed lines in (b), (d), and (f) denote the Page value of von Neumann EE $S_{\text{Page}}=\ln m-m/2n$ with $m=2^l$ and $n=2^{N-l}$ ($N=12$ as the number of qubit). The dotted curve in (e) shows the numerics considering decoherence. The dashed lines in (g) are the linear fittings of the experimental data. The error bars of experimental data are smaller than the size of the symbols.

Figure 4

Information scrambling quantified by TMI. (a) The schematic experimental pulse sequence for the dynamics of TMI for the qubit chain. Panel (b) is similar to (a) but for the qubit ladder. (c) Numerical results of the time evolution of TMI for the qubit chain and ladder, without considering decoherence, of which the averaged values are $-0.283$ and $-0.426$ (highlighted by the dashed lines), respectively. (d) The experimental data of the time evolution of TMI for the qubit chain and ladder, of which the averaged values are $-0.106$ and $-0.196$ (highlighted by the dashed lines), respectively. The error bars of experimental data are smaller than the size of the symbols.