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

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_2timesmathbb Z₂-protected Haldane phase, showing that it is determined by the post-measurement 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.