Finding flows in the one-way measurement model
arXiv:quant-ph/0611284 · doi:10.1103/PhysRevA.77.022328
Abstract
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform a unitary embedding between two Hilbert spaces is for the graph G, together with input/output vertices I, O \subset V(G), to have a flow in the sense introduced by Danos and Kashefi [quant-ph/0506062]. For the special case of |I| = |O|, using a graph-theoretic characterization, I show that such flows are unique when they exist. This leads to an efficient algorithm for finding flows, by a reduction to solved problems in graph theory.
8 pages, 3 figures: somewhat condensed and updated version, to appear in PRA
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Cited by in corpus (18)
- Generalized Flow and Determinism in Measurement-based Quantum Computation
- Parallelizing Quantum Circuits
- Finding Optimal Flows Efficiently
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- Relating Measurement Patterns to Circuits via Pauli Flow
- An analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation
- Minimal physical resources for the realisation of measurement-based quantum computation
- A complete algorithm to find flows in the one-way measurement model
- Geometry-Based Optimization of One-Way Quantum Computation Measurement Patterns
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- Simple procedure for classical signal-procession in cluster-state quantum computation
- Quadratic Form Expansions for Unitaries
- An extremal result for geometries in the one-way measurement model