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

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.

17 pages, 9 figures

References in corpus (31)

• The density-matrix renormalization group in the age of matrix product states
• Persistent entanglement in arrays of interacting particles
• Quantum Teleportation is a Universal Computational Primitive
• Measurement-based quantum computation with cluster states
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• The ITensor Software Library for Tensor Network Calculations
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Zoo of quantum-topological phases of matter
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classifying quantum phases using Matrix Product States and PEPS
• Criticality, the area law, and the computational power of PEPS
• String order and symmetries in quantum spin lattices
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Symmetry-protected phases for measurement-based quantum computation
• Quantum computation on the edge of a symmetry-protected topological order
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Computational Power of Symmetry-Protected Topological Phases
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Quantum computational renormalization in the Haldane phase
• Symmetry-protected topological phases with uniform computational power in one dimension
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Spin-1 Haldane phase in a chain of Rydberg atoms
• Quantum Simulation of Spin-1 XXZ-Heisenberg Models and the Haldane Phase with Dysprosium
• The Fidelity of Measurement-Based Quantum Computation under a Boson Environment
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems