Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy

TL;DR

This paper shows that the ground state of a spin-1 XXZ chain in the Haldane phase can be used as a resource for measurement-based quantum computation, achieving high-fidelity single-qubit gates.

Contribution

It introduces a method to implement high-fidelity single-qubit gates using the ground state of a spin-1 XXZ chain with anisotropies in the Haldane phase, with an analytic expression for gate fidelity.

Findings

Gate fidelity exceeds 0.99 with proper tuning of parameters.

Fidelity is determined by spin-spin correlations and failure probability.

Enhancement of fidelity is due to strengthened antiferromagnetic correlations.

Abstract

We demonstrate that the ground state of a spin-1 $XXZ$ chain with uniaxial anisotropies, single-ion anisotropy $D$ and Ising-like anisotropy $J$, within the Haldane phase can serve as a resource state for measurement-based quantum computation implementing single-qubit gates. The gate fidelity of both elementary rotation gates and general single-qubit unitary gates composed of rotations about the $x$, $y$, and $z$ axes is evaluated, and is found to exceed 0.99 when $D$ or $J$ is appropriately tuned. Furthermore, we derive an analytic expression for the rotation-gate fidelity under the assumption that the state lies within the $\mathbb Z_2\times \mathbb Z_2$-protected Haldane phase, showing that it is determined by the postmeasurement spin-spin correlation function and the failure probability. The observed enhancement of gate fidelity in the spin-1 $XXZ$ chain originates from the strengthening of antiferromagnetic (AFM) correlations near the AFM phase, which effectively suppresses failure states.