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arXiv:1704.07378 · International Journal of Theoretical Physics

Optimization of One-Way Quantum Computation Measurement Patterns

Maryam Eslamy, Mahboobeh Houshmand, Morteza Saheb Zamani, Mehdi Sedighi

Published Sep 3, 2018• 7 citations
arXivHTMLPDF
DOI
10.1007/s10773-018-3844-x

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We introduce an open-source software library Graphix, which optimizes and simulates measurement-based quantum computation (MBQC). By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical preprocessing of Pauli measurements in the measurement patterns, significantly reducing the number of operations required to perform the quantum computation while maintaining determinism. For a measurement pattern translated from a quantum circuit, this corresponds to the preprocessing of all Clifford gates, and this improvement in the one-way model is important for efficient operations in quantum hardware with limited qubit numbers. In addition to the direct translation from gate networks, we provide a pattern generation method based on flow-finding algorithms, which automatically generates byproduct correction sequences to ensure determinism. We further implement optimization strategies for measurement patterns beyond the standardization procedure and provide tensor-network backend for classically simulating the MBQC.
In the model of measurement-based quantum computing (MBQC), computations are performed via sequential measurements on a highly entangled graph state. MBQC is a natural model for photonic quantum computing and has been shown to be useful for tasks like optimization and verification of general quantum computations. Therefore, it is often necessary to translate between MBQC and the predominantly used quantum circuit model in a fast and reliable way. While there are algorithms with linear complexity to extract quantum circuits from measurement patterns using additional ancilla qubits, efficient ancilla-free extraction has shown to be more costly. We develop strategies to parallelize an existing extraction algorithm based on ZX-calculus by exploiting the graph structure of measurement patterns and evaluate the performance on patterns obtained from a benchmark set of quantum circuits. Our results suggest that possible parallelization speedups are closely related to the graph structure of a pattern.
In one-way quantum computation (1WQC) model, 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. The needed computations are organized as measurement patterns or simply patterns in the 1WQC model. The entanglement operations in a pattern can be shown by a graph which together with the set of its input and output qubits is called the geometry of the pattern. Causal flow is a sufficient condition to identify a dependency structure for measurement sequences in order to obtain determinism. Signal shifting is an optimization technique which uses a set of rewrite rules to propagate the Pauli-Z corrections on the measured qubits to the end of patterns. However, automatically applying these rules has difficulties for implementation and is time consuming due to using many ineffective commutation rules. To overcome this problem, in this paper, a new automatic approach is proposed to perform signal shifting on patterns with flows based on their geometries instead of using rewriting rules. It is shown that the time complexity of the proposed approach is improved compared to the previous ones.