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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2405.18143 |
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| _version_ | 1866929362269372416 |
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| author | Schwetz, Maximilian Noack, Reinhard M. |
| author_facet | Schwetz, Maximilian Noack, Reinhard M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simon algorithm in measurement-based quantum computing Schwetz, Maximilian Noack, Reinhard M. Quantum Physics 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. |
| title | Simon algorithm in measurement-based quantum computing |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.18143 |