Phase map decompositions for unitaries

Abstract

We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based model for quantum computing. Specifically, we show how to extract from such a decomposition a matching entangled graph state (with inputs), and a set of measurements angles, when there is one. Next, we check whether the obtained graph state verifies a "flow" condition, which guarantees an execution order such that the dependent measurements and corrections of the pattern yield deterministic results. Using a graph theoretic characterization of flows, we can determine whether a flow can be constructed for a graph state in polynomial time. This approach yields an algorithmic procedure which, when it succeeds, may produce an efficient pattern for a given unitary.

17 pages: earlier version submitted to ICALP 2006

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Cited by in corpus (8)

• Determinism in the one-way model
• Generalized Flow and Determinism in Measurement-based Quantum Computation
• Parallelizing Quantum Circuits
• Finding flows in the one-way measurement model
• Information Flow in Secret Sharing Protocols
• A complete algorithm to find flows in the one-way measurement model
• Quadratic Form Expansions for Unitaries
• An extremal result for geometries in the one-way measurement model