A Quantum Approximate Optimization Method For Finding Hadamard Matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910647969644544 |
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| author | Suksmono, Andriyan Bayu |
| author_facet | Suksmono, Andriyan Bayu |
| contents | Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts using a quantum annealer were impeded by the limitations of the present quantum resource and its capability to implement high order interaction terms, which for an $M$-order matrix will grow by $O(M^2)$. In this paper, we propose a novel qubit-efficient method by implementing the Hadamard matrix searching algorithm on a gate-based quantum computer. We achieve this by employing the Quantum Approximate Optimization Algorithm (QAOA). Since high order interaction terms that are implemented on a gate-based quantum computer do not need ancillary qubits, the proposed method reduces the required number of qubits into $O(M)$. We present the formulation of the method, construction of corresponding quantum circuits, and experiment results in both a quantum simulator and a real gate-based quantum computer. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_07964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Quantum Approximate Optimization Method For Finding Hadamard Matrices Suksmono, Andriyan Bayu Quantum Physics Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts using a quantum annealer were impeded by the limitations of the present quantum resource and its capability to implement high order interaction terms, which for an $M$-order matrix will grow by $O(M^2)$. In this paper, we propose a novel qubit-efficient method by implementing the Hadamard matrix searching algorithm on a gate-based quantum computer. We achieve this by employing the Quantum Approximate Optimization Algorithm (QAOA). Since high order interaction terms that are implemented on a gate-based quantum computer do not need ancillary qubits, the proposed method reduces the required number of qubits into $O(M)$. We present the formulation of the method, construction of corresponding quantum circuits, and experiment results in both a quantum simulator and a real gate-based quantum computer. |
| title | A Quantum Approximate Optimization Method For Finding Hadamard Matrices |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.07964 |