Simon algorithm in measurement-based quantum computing

• URL: http://arxiv.org/abs/2405.18143v1
• Date: Tue, 28 May 2024 13:02:54 GMT
• Title: Simon algorithm in measurement-based quantum computing
• Authors: Maximilian Schwetz, Reinhard M. Noack,
• Abstract summary: Simon's subgroup hidden algorithm was the first quantum algorithm to prove the superiority of quantum computing over classical computing. We present a reformulation of the Simon algorithm into the language of measurement-based quantum computing. We show that the $n$-qubit version of the Simon algorithm can be formulated in MBQC as cluster state graph with $2n$ nodes and $n2$ edges.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simon's hidden subgroup algorithm was the first quantum algorithm to prove the superiority of quantum computing over classical computing in terms of complexity. Measurement-based quantum computing (MBQC) is a formulation of quantum computing that, while equivalent in terms of computational power, can be advantageous in experiments and in displaying the core mechanics of quantum algorithms. We present a reformulation of the Simon algorithm into the language of MBQC -- in detail for two qubits and schematically for $n$ qubits. We utilize the framework of ZX-calculus, a graphical tensor description of quantum states and operators, to translate the circuit description of the algorithm into a form concordant with MBQC. The result for the two-qubit Simon algorithm is a ten-qubit cluster state on which single-qubit measurements suffice to extract the desired information. Additionally, we show that the $n$-qubit version of the Simon algorithm can be formulated in MBQC as cluster state graph with $2n$ nodes and $n^2$ edges. This is an example of the MBQC formulation of a quantum algorithm that is exponentially faster than its classical counterpart. As such, this formulation should aid in understanding the core mechanics of such an established algorithm and could serve as a blueprint for experimental implementation.

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