Abstract
Recent quantum simulation by Google [Nature 612, 240 (2022)] has demonstrated the formation of bound states of interacting photons in a quantum-circuit version of the XXZ spin chain. While such bound states are protected by integrability in a one-dimensional chain, the experiment found the bound states to be unexpectedly robust when integrability was broken by decorating the circuit with additional qubits, at least for small numbers of qubits () within the experimental capability. Here we scrutinize this result by state-of-the-art classical simulations, which greatly exceed the experimental system sizes and provide a benchmark for future studies in larger circuits. We find that the bound states consisting of a finite number of photons are indeed robust in the nonintegrable regime, even after scaling to the infinite-time and infinite-system size limit. Moreover, we show that such systems possess unusual spectral properties, with level statistics that deviates from the random matrix theory expectation. On the other hand, for low but finite density of photons, we find a much faster onset of thermalization and significantly weaker signatures of bound states, suggesting that anomalous dynamics may only be a property of dilute systems with zero density of photons in the thermodynamic limit. The robustness of the bound states is also influenced by the number of decoration qubits and, to a lesser degree, by the regularity of their spatial arrangement.
- Received 6 July 2023
- Accepted 20 December 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010316
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Recent advances in quantum simulation are allowing the probe of fundamental physics in previously inaccessible regimes. One important question concerns the existence of bound states in many-particle systems. Bound states play a key role in weakly interacting quantum systems, such as an electron bound to the atomic nucleus via Coulomb force. In a recent experiment, Google Quantum AI has realized a variant of the XXZ model—a celebrated model of quantum magnetism known to support multiparticle bound states. Surprisingly, the bound states remained robust even when the quantum circuit was “decorated” by additional qubits, profoundly changing its structure. This posed an intriguing question: Under what conditions do the bound states remain resilient to perturbations?
We performed state-of-the-art classical simulations of Google’s experiment, accessing the infinite-time and infinite-circuit limits, which are beyond the current experimental capability. We confirmed the robustness of the bound states, but only in the dilute limit containing a few particles. On the other hand, we showed that fast thermalization is restored in bound states containing a finite density of particles in the thermodynamic limit. Furthermore, we explored alternative setups, such as varying the number of decorations and their spatial arrangements, formulating concrete predictions for the stability of bound states in each case.
By greatly exceeding the capabilities of quantum hardware, our work provides useful benchmarks for future quantum simulations. The identification of several previously unknown anomalous spectral properties of decorated XXZ circuits paves the way toward a general theory of the stability of few-particle bound states in nonintegrable many-body systems.
