Profusion of Symmetry-Protected Qubits from Stable Ergodicity Breaking

TL;DR

This paper demonstrates how combining discrete symmetries with topological Hilbert space fragmentation can create exponentially many stable qubits, enhancing robustness but limiting quantum error correction capabilities.

Contribution

It introduces a novel approach to generate topologically stable qubits using symmetry-protected Hilbert space fragmentation, exemplified by the $\

Findings

Exponential number of stable qubits achieved.

Encoded qubits are robust to symmetry-respecting perturbations.

Universal transversal logical gates are implementable on qubit pairs.

Abstract

We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example of the $\mathsf{CZ}_p$ model, where the encoded qubits are stable to arbitrary symmetry-respecting perturbations for parametrically long times, substantially enhancing the robustness of a recently proposed construction based on nontopological fragmentation. In this model, the encoded qubits naturally come in pairs for which a universal set of transversal logical gates can be performed, ruling out (by the Eastin-Knill theorem) the possibility of using them for quantum error correction. We also comment on the combination of symmetry enrichment and topological fragmentation more generally, and the implications for use of systems exhibiting Hilbert space fragmentation as quantum memories.