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Optimization of One-Way Quantum Computation Measurement Patterns

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Abstract

In one-way quantum computation (1WQC), an initial highly entangled state, called a graph state, is used to perform universal quantum computations by a sequence of adaptive single-qubit measurements and post-measurement Pauli-X and Pauli-Z corrections. 1WQC computation can be represented by a measurement pattern (or simply a pattern). The entanglement operations in a pattern can be shown by a graph which together with the identified set of its input and output qubits is called the geometry of the pattern. Since a pattern is based on quantum measurements, which are fundamentally nondeterministic evolutions, there must be conditions over geometries to guarantee determinism. These conditions are formalized by the notions of flow and generalized flow (gflow). Previously, three optimization methods have been proposed to optimize 1WQC patterns which can be performed using the measurement calculus formalism by rewriting rules. However, the serial implementation of these rules is time consuming due to executing many ineffective commutation rules. To overcome this problem, in this paper, a new scheme is proposed to perform the optimization techniques simultaneously on patterns with flow and only gflow based on their geometries. Furthermore, the proposed scheme obtains the maximally delayed gflow order for geometries with flow. It is shown that the time complexity of the proposed approach is improved over the previous ones.

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Notes

  1. As gflow is more general than flow, in the rest of the paper we will use gflow only in reference to open graphs which do not have flow.

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Authors and Affiliations

  1. Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran

    Maryam Eslamy, Morteza Saheb Zamani & Mehdi Sedighi

  2. Department of Computer Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Mahboobeh Houshmand

Authors
  1. Maryam Eslamy
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  2. Mahboobeh Houshmand
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  3. Morteza Saheb Zamani
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  4. Mehdi Sedighi
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Correspondence to Mahboobeh Houshmand.

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Eslamy, M., Houshmand, M., Zamani, M.S. et al. Optimization of One-Way Quantum Computation Measurement Patterns. Int J Theor Phys 57, 3296–3317 (2018). https://doi.org/10.1007/s10773-018-3844-x

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  • DOI: https://doi.org/10.1007/s10773-018-3844-x

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