Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states

Abstract

We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the square lattice is a universal resource for the measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 POVM on all spins. We also argue that the spin-2 AKLT state on the three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region that the ground state can still support a universal resource before making a transition in its quantum computational power.

17 pages, 8 figures, PRA accepted version

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Cited by in corpus (28)

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• Universal quantum computation using fractal symmetry-protected cluster phases
• Symmetry-protected topological phases with uniform computational power in one dimension
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Qudit quantum computation on matrix product states with global symmetry
• Symmetry-protected topologically ordered states for universal quantum computation
• Measurement-Based Quantum Computation
• Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Quantum spin systems for measurement-based quantum computation
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• AKLT models on decorated square lattices are gapped
• Exact stabilization of entangled states in finite time by dissipative quantum circuits
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Quantum algorithm for preparing the ground state of a system via resonance transition
• Quantitatively improved finite-size criteria for spectral gaps
• Competing valence bond and symmetry breaking Mott states of spin-3/2 fermions on a honeycomb lattice
• The Gauge Theory of Measurement-Based Quantum Computation
• Phase transitions of a 2D deformed-AKLT model
• Classification of measurement-based quantum wire in stabilizer PEPS
• Spectral properties for a family of two-dimensional quantum antiferromagnets
• Quantum compiling with a variational instruction set for accurate and fast quantum computing