Quantum computation on the edge of a symmetry-protected topological order

TL;DR

This paper proposes a method for quantum computation using the edge states of a symmetry-protected topological phase, enabling universal quantum logic through boundary measurements in a robust, entangled system.

Contribution

It introduces a simple adiabatic spin extraction primitive that makes ground states of the Haldane phase useful as quantum wires, leveraging topological protection and boundary entanglement.

Findings

Primitive enables universal quantum computation on the edge states.

Compatible with discrete symmetries protecting topological order.

Demonstrates a holographic principle linking boundary and bulk quantum information.

Abstract

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin adiabatically from the bulk followed by its measurement, is shown to make any ground state of the one-dimensional isotropic Haldane phase useful ubiquitously as a quantum logical wire. The primitive is compatible with certain discrete symmetries that protect this topological order, and the antiferromagnetic Heisenberg spin-1 finite chain is practically available. Our approach manifests a holographic principle in that the logical information of a universal quantum computer can be written and processed perfectly on the edge state (i.e., boundary) of the system, supported by the persistent entanglement from the bulk even when the ground state and its evolution cannot be exactly analyzed.