Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
arXiv:1612.08135 · doi:10.1103/PhysRevLett.120.170503
Abstract
An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.
arXiv comment17 pages, 4 figures. v2: published version, contains a new appendix dealing with renormalization methods
References in corpus (54)
- Quantum Simulation
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Persistent entanglement in arrays of interacting particles
- Periodic table for topological insulators and superconductors
- 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
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Symmetry protection of topological order in one-dimensional quantum spin systems
- Classifying quantum phases using Matrix Product States and PEPS
- Stabilizer Codes and Quantum Error Correction
- Valence Bond Solids for Quantum Computation
- Novel schemes for measurement-based quantum computation
- Universal resources for measurement-based quantum computation
- Measurement-based quantum computation beyond the one-way model
- Long-range quantum entanglement in noisy cluster states
- Quantum Hypergraph States
- Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
- Symmetry-protected phases for measurement-based quantum computation
- Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
- Quantum computation based on d-level cluster states
- Quantum computation on the edge of a symmetry-protected topological order
- Identifying phases of quantum many-body systems that are universal for quantum computation
- An introduction to measurement based quantum computation
- Quantum phase transition between cluster and antiferromagnetic states
- Quantum computational capability of a 2D valence bond solid phase
- Topological interactions in broken gauge theories
- Topological color code and symmetry-protected topological phases
- Hierarchy of universal entanglement in 2D measurement-based quantum computation
- Fundamentals of universality in one-way quantum computation
- Computational Power of Symmetry-Protected Topological Phases
- Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation
- Universal quantum computer from a quantum magnet
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Resource quality of a symmetry-protected topologically ordered phase for quantum computation
- Symmetry protected topological order at nonzero temperature
- Entanglement and nonclassical properties of hypergraph states
- Gapped boundaries, group cohomology and fault-tolerant logical gates
- Quantum computational renormalization in the Haldane phase
- Detecting two dimensional symmetry protected topological order in a ground state wave function
- Symmetry-protected topological phases with uniform computational power in one dimension
- Symmetry protection of measurement-based quantum computation in ground states
- Measurement-based quantum computation in a 2D phase of matter
- Fate of the cluster state on the square lattice in a magnetic field
- Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
- Symmetry-protected topologically ordered states for universal quantum computation
- Quantum state reduction for universal measurement based computation
- Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
- Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
- Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
- Qudit Hypergraph States
- Bounds on universal quantum computation with perturbed 2d cluster states
- Transitions in the quantum computational power
Cited by in corpus (24)
- Many-body quantum magic
- Quantum complexity and topological phases of matter
- A computationally universal phase of quantum matter
- Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
- Universal quantum computation using fractal symmetry-protected cluster phases
- Efficient Verification of Hypergraph States
- Symmetry-protected sign problem and magic in quantum phases of matter
- Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
- Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
- Universal measurement-based quantum computation in two-dimensional SPT phases
- Resource theory of quantum uncomplexity
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- Magic of quantum hypergraph states
- Universal quantum computing using symmetry-protected topologically ordered states
- Entanglement of random hypergraph states
- Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
- Quantum Hypergraph States in Continuous Variables
- Complexity-constrained quantum thermodynamics
- Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation
- Many-body quantum catalysts for transforming between phases of matter
- Redundant string symmetry-based error correction: Demonstrations on quantum devices
- Toward a physically motivated notion of Gaussian complexity geometry
- Attention to Quantum Complexity
- Nonunitary gates using measurements only