Quantum computational renormalization in the Haldane phase

TL;DR

This paper demonstrates that single-spin measurements on the ground state of a spin-1 chain can perform renormalization-like transformations, making quantum computational capabilities robust within the Haldane phase.

Contribution

It introduces a method to use measurements to mimic renormalization group transformations, enhancing the robustness of quantum computation in spin lattice phases.

Findings

Quantum measurements can simulate renormalization group transformations.

The ground state of a spin-1 chain acts as a quantum computational wire.

Robust quantum computation is possible throughout the Haldane phase.

Abstract

Single-spin measurements on the ground state of an interacting spin lattice can be used to perform a quantum computation. We show how such measurements can mimic renormalization group transformations and remove the short-ranged variations of the state that can reduce the fidelity of a computation. This suggests that the quantum computational ability of a spin lattice could be a robust property of a quantum phase. We illustrate our idea with the ground state of a spin-1 chain, which can serve as a quantum computational wire not only at the Affleck-Kennedy-Lieb-Tasaki point, but within the rotationally-invariant Haldane phase.