Qudit quantum computation on matrix product states with global symmetry

Abstract

Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the 1D qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.

References in corpus (46)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum Teleportation is a Universal Computational Primitive
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classifying quantum phases using Matrix Product States and PEPS
• Methodology for quantum logic gate constructions
• Sequential generation of entangled multi-qubit states
• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• 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
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Quantum computational capability of a 2D valence bond solid phase
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• An order parameter for symmetry-protected phases in one dimension
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• On topological phases of spin chains
• Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Symplectic N and time reversal in frustrated magnetism
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Symmetry-protected topological phases with uniform computational power in one dimension
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Quantum computational webs
• Entanglement in an SU(n) Valence-Bond-Solid State
• Measurement-based quantum computation in a 2D phase of matter
• From symmetry-protected topological order to Landau order
• A 2 rebit gate universal for quantum computing
• Valence bond solid states with symplectic symmetry
• SU(6) Heisenberg model on the honeycomb lattice: competition between plaquette and chiral order
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Valence bond solid formalism for d-level one-way quantum computation
• Quantum state reduction for universal measurement based computation
• Hybrid valence-bond states for universal quantum computation
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$

Cited by in corpus (22)

• Integrated micro-comb sources for quantum optical applications
• Computational Power of Symmetry-Protected Topological Phases
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Quasi-exact quantum computation
• Topological qubits from valence bond solids
• Choi states, symmetry-based quantum gate teleportation, and stored-program quantum computing
• Universal resources for quantum computing
• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• Quantum computation by teleportation and symmetry
• Qudit low-density parity-check codes
• Qubit-qudit entanglement transfer in defect centers with high-spin nuclei
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Measurement-based quantum computing with qudit stabilizer states
• Resource-efficient entanglement detection in high-dimensional states via two-qubit witnesses
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Qudit Noisy Stabilizer Formalism
• A quantum number theory