Symmetry protection of measurement-based quantum computation in ground states

Abstract

The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove that, provided the perturbation is sufficiently small and respects a certain symmetry, the perturbed ground state remains a universal resource. We do this by characterising the operation of an adaptive measurement protocol throughout a suitable symmetry-protected quantum phase, relying on generic properties of the phase rather than any analytic control over the ground state.

20 pages plus appendices, 11 figures, comments very welcome; v2 minor corrections and additional references; v3 published version with minor corrections

References in corpus (14)

• Matrix product states represent ground states faithfully
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Valence Bond Solids for Quantum Computation
• String order and symmetries in quantum spin lattices
• Novel schemes for measurement-based quantum computation
• Localizable Entanglement
• Measurement-based quantum computation beyond the one-way model
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum computational capability of a 2D valence bond solid phase
• First order phase transition in the anisotropic quantum orbital compass model
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Fate of the cluster state on the square lattice in a magnetic field
• Quantum computation via measurements on the low-temperature state of a many-body system
• Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions

Cited by in corpus (19)

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• MERA for Spin Chains with Continuously Varying Criticality
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Playing quantum nonlocal games with six noisy qubits on the cloud
• Fractionalization of subsystem symmetries in two dimensions
• 3-Fermion topological quantum computation
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Hierarchies of resources for measurement-based quantum computation
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• The abelian state hidden subgroup problem: Learning stabilizer groups and beyond
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity