Exploring nontrivial topology at quantum criticality in a superconducting processor

TL;DR

This study uses a superconducting quantum processor with up to 100 qubits to experimentally explore nontrivial topological states at quantum criticality, revealing boundary properties and topological degeneracies.

Contribution

It develops an efficient method to probe topological features of critical states and verifies the bulk-boundary correspondence in a quantum simulator setting.

Findings

Identified nontrivial topology in critical states using boundary g-function measurements.

Observed two-fold topological degeneracy in the entanglement spectrum.

Demonstrated the utility of low-lying critical states for studying topology and quantum criticality.

Abstract

The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk energy gap. However, realizing and characterizing such topologically nontrivial quantum critical states with large particle numbers remains an outstanding experimental challenge in statistical and condensed matter physics. Programmable quantum processors can directly prepare and manipulate exotic quantum many-body states, offering a powerful path for exploring the physics behind these states. Here, we present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits. We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, by adapting the entanglement Hamiltonian tomography technique, we recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary condition, experimentally verifying the universal bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.