Topological magic response in quantum spin chains

TL;DR

This paper introduces the concept of topological magic response in quantum spin chains, revealing how certain topological phases exhibit non-local quantum correlations when perturbed by non-Clifford circuits, with potential implications for quantum error correction.

Contribution

It defines and analyzes topological magic response, a new probe for non-local quantum correlations in topological phases, using stabilizer Rényi entropies and exact computational methods.

Findings

SPT phases show a robust topological magic response.

Trivial phases lack topological magic response.

The response distinguishes topological from trivial phases.

Abstract

Topological matter provides natural platforms for robust, non-local information storage, central to quantum error correction. Yet, while the relation between entanglement and topology is well established, little is known about the role of nonstabilizerness (or magic), a pivotal concept in fault-tolerant quantum computation, in topological phases. We introduce the concept of topological magic response, the ability of a state to spread over stabilizer space when perturbed by finite-depth non-Clifford circuits. Unlike a topological invariant or order parameter, this response function probes how a phase reacts to non-Clifford perturbations, revealing the presence of non-local quantum correlations. In Ising-type spin chains, we show that symmetry-broken and paramagnetic phases lack such a response, whereas symmetry-protected topological (SPT) phases always display it. To capture this, we utilize a combination of stabilizer R\'{e}nyi entropies that, in analogy with topological entanglement entropy, isolates non-locally stored information. Using exact analytic computations and matrix product states simulations based on an algorithmic technique we introduce, we show that SPT phases doped with $T$ gates support robust topological magic response, while trivial phases remain featureless.