Valence bond solid formalism for d-level one-way quantum computation

Abstract

The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.

26 pages, 9 figures. Published in Journal of Physics A: Mathematical and General

References in corpus (8)

• Experimental One-Way Quantum Computing
• Resource-efficient linear optical quantum computation
• Valence Bond Solids for Quantum Computation
• Fault-tolerant quantum computation with cluster states
• Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic
• Unified derivations of measurement-based schemes for quantum computation
• Entanglement in a Valence-Bond-Solid State
• Computation by measurements: a unifying picture

Cited by in corpus (23)

• Universal Quantum Computation with Continuous-Variable Cluster States
• A universal qudit quantum processor with trapped ions
• Building Gaussian Cluster States by Linear Optics
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
• Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
• Qudit quantum computation on matrix product states with global symmetry
• Symmetry-protected topologically ordered states for universal quantum computation
• Complexity and entanglement in non-local computation and holography
• Hybrid controlled-SUM gate with one superconducting qutrit and one cat-state qutrit and application in hybrid entangled state preparation
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Qudit hypergraph states and their properties
• Adaptive Compilation of Multi-Level Quantum Operations
• Pauli-based model of quantum computation with higher-dimensional systems
• Single-copy entanglement in a gapped quantum spin chain
• Decoherence-based exploration of d-dimensional one-way quantum computation
• Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
• Complete ZX-calculi for the stabiliser fragment in odd prime dimensions
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Measurement-based quantum computing with qudit stabilizer states
• Blind quantum computing with different qudit resource state architectures