Quantum computational renormalization in 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.

v2: 4 pages, 3 figures; improved description of buffering scheme and connection to string operators. v3: final published version

References in corpus (14)

• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• Localizable Entanglement
• Universal resources for measurement-based quantum computation
• Measurement-based quantum computation beyond the one-way model
• Implementation of Spin Hamiltonians in Optical Lattices
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum computation on the edge of a symmetry-protected topological order
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Designing spin-1 lattice models using polar molecules
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Phase transition of computational power in the resource states for one-way quantum computation
• Quantum state reduction for universal measurement based computation

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• Hybrid valence-bond states for universal quantum computation
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• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Quantum information in the Posner model of quantum cognition
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
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• Designing a polymerized phenalenyl tessellation molecule to realize a super-honeycomb antiferromagnetic S = 3/2 spin system
• Quantum phase with spontaneous translational symmetry breaking in an extended diamond chain
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Sub-Riemannian geometry of measurement based quantum computation
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Characterization of localized effective spins in gapped quantum spin chains