Symmetry-protected topological phases with uniform computational power in one dimension

Abstract

We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation.

Also see the companion paper Ref [24] by D. Stephen et al., submitted in parallel. The main purpose of the present article is to put in place the computational primitives for MBQC using resource states located anywhere within given SPTO phases. Ref [24] describes in greater detail how the group of MBQC-simulable gates relates to the cohomological description of the corresponding SPTO phases

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• Universal quantum computation using fractal symmetry-protected cluster phases
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Symmetry-protected sign problem and magic in quantum phases of matter
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Qudit quantum computation on matrix product states with global symmetry
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
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• Quantum spin systems for measurement-based quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Observing Floquet topological order by symmetry resolution
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Unwinding Short-Range Entanglement
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• The role of cohomology in quantum computation with magic states
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• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Topological Floquet interface states in optical fibre loops
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Contextuality and bundle diagrams
• Harnessing symmetry-protected topological order for quantum memories
• The Gauge Theory of Measurement-Based Quantum Computation
• Pivoting through the chiral-clock family
• Classification of measurement-based quantum wire in stabilizer PEPS
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Quantum teleportation implies symmetry-protected topological order
• Counter-intuitive yet efficient regimes for measurement based quantum computation on symmetry protected spin chains
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Measurement-Induced Entanglement in Conformal Field Theory
• Nonunitary gates using measurements only
• Sub-Riemannian geometry of measurement based quantum computation
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity