Fate of the cluster state on the square lattice in a magnetic field

Abstract

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.

arXiv comment12 pages, 9 figures

References in corpus (31)

• Fault-tolerant quantum computation by anyons
• Elementary gates for quantum computation
• Measurement-based quantum computation
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A Rydberg Quantum Simulator
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The iTEBD algorithm beyond unitary evolution
• A fault-tolerant one-way quantum computer
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Valence Bond Solids for Quantum Computation
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Robustness of a perturbed topological phase
• Ground state fidelity from tensor network representations
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Quantum phase transition between cluster and antiferromagnetic states
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• The Structure of Operators in Effective Particle-Conserving Models
• Self-duality and bound states of the toric code model in a transverse field
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• First order phase transition in the anisotropic quantum orbital compass model
• Breakdown of a perturbed Z_N topological phase
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions

Cited by in corpus (30)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Algorithms for finite Projected Entangled Pair States
• Subsystem symmetry protected topological order
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Symmetry protection of measurement-based quantum computation in ground states
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Subsystem symmetry enriched topological order in three dimensions
• Gauging tensor networks with belief propagation
• Tensor Networks contraction and the Belief Propagation algorithm
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Local response of topological order to an external perturbation
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Local convertibility of the ground state of the perturbed Toric code
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Duality viewpoint of criticality
• The minimal canonical form of a tensor network
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Bounds on universal quantum computation with perturbed 2d cluster states
• Topological Phase Transition in the Extended Cluster Compass Ladder
• Linked Cluster Expansions via Hypergraph Decompositions
• Quantum phase transitions in the $K$-layer Ising toric code
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Loop update for infinite projected entangled-pair states in two spatial dimensions
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Scalable projected entangled-pair state representation of random quantum circuit states
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet
• Duality in spin systems via the $SU(4)$ algebra