A computationally universal phase of quantum matter

Abstract

We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground state is a universal resource for measurement based quantum computation.

arXiv comment5 + 2 pages

References in corpus (28)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Novel schemes for measurement-based quantum computation
• Symmetry-protected phases for measurement-based quantum computation
• Topological phases with generalized global symmetries
• Index theory of one dimensional quantum walks and cellular automata
• Quantum computation on the edge of a symmetry-protected topological order
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• Computational Power of Symmetry-Protected Topological Phases
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Symmetry protected topological order at nonzero temperature
• The topological classification of one-dimensional symmetric quantum walks
• Quantum circuit complexity of one-dimensional topological phases
• Quantum computation via translation-invariant operations on a chain of qubits
• Symmetry-protected topological phases with uniform computational power in one dimension
• Symmetry protection of measurement-based quantum computation in ground states
• On the structure of Clifford quantum cellular automata
• Measurement-based quantum computation in a 2D phase of matter
• Symmetry-protected topologically ordered states for universal quantum computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems

Cited by in corpus (72)

• Many-body quantum magic
• Identification of symmetry-protected topological states on noisy quantum computers
• Long-range entanglement from measuring symmetry-protected topological phases
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Spurious topological entanglement entropy from subsystem symmetries
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Anomaly Inflow for Subsystem Symmetries
• Speed limits and locality in many-body quantum dynamics
• Symmetry protected topological phases under decoherence
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Universal fault-tolerant measurement-based quantum computation
• Symmetry-protected sign problem and magic in quantum phases of matter
• Symmetry-protected self-correcting quantum memories
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Subsystem symmetry enriched topological order in three dimensions
• Searching for Fracton Orders via Symmetry Defect Condensation
• Classifying local fractal subsystem symmetry protected topological phases
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Detecting subsystem symmetry protected topological order via entanglement entropy
• 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
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Complexity phase diagram for interacting and long-range bosonic Hamiltonians
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• A comparative study of universal quantum computing models: towards a physical unification
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• The role of cohomology in quantum computation with magic states
• Symmetries and entanglement of stabilizer states
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Inaccessible entanglement in symmetry protected topological phases
• Fractionalization of subsystem symmetries in two dimensions
• Universal structure of measurement-induced information in many-body ground states
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• 3-Fermion topological quantum computation
• Fractalizing quantum codes
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Fracton-like phases from subsystem symmetries
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Hierarchies of resources for measurement-based quantum computation
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Universal resources for quantum computing
• The Gauge Theory of Measurement-Based Quantum Computation
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• Variational measurement-based quantum computation for generative modeling
• Classification of measurement-based quantum wire in stabilizer PEPS
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Quantum computation by teleportation and symmetry
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Nearly optimal time-independent reversal of a spin chain
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Measurement-based quantum computation from Clifford quantum cellular automata
• Many-body quantum catalysts for transforming between phases of matter
• Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• 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
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Measurement-Induced Entanglement in Conformal Field Theory
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Sub-Riemannian geometry of measurement based quantum computation
• Nonunitary gates using measurements only
• Scaling of Computational Order Parameters in Rydberg Atom Graph States