Resource quality of a symmetry-protected topologically ordered phase for quantum computation

TL;DR

This paper demonstrates that the 1D symmetry-protected topologically ordered phase with octahedral symmetry can serve as a robust resource for quantum computation, enabling high-fidelity one-qubit gates through its intrinsic entanglement properties.

Contribution

It shows that the entire phase possesses the capability for universal quantum gates, linking topological order with quantum computational utility.

Findings

Ground states can implement any one-qubit gate asymptotically.

Perfect gate fidelity aligns with string order parameters.

Operational utility is intrinsic to the phase, not just specific states.

Abstract

We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as certain characteristic lengths are finite, all its ground states have the capability to implement any unit-fidelity one-qubit gate operation asymptotically as a key computational building block. This feature is intrinsic to the entire phase, in that perfect gate fidelity coincides with perfect string order parameters under a state-insensitive renormalization procedure. Our approach may pave the way toward a novel program to classify quantum many-body systems based on their operational use for quantum information processing.