A quantum approximate optimization method for finding Hadamard matrices

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, wh...

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Veröffentlicht in:	Scientific reports Jg. 15; H. 1; S. 33254 - 16
1. Verfasser:	Suksmono, Andriyan Bayu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	London Nature Publishing Group UK 26.09.2025 Nature Publishing Group Nature Portfolio
Schlagworte:	639/166/987 639/766/483/481 Algorithms Approximation Boolean Circuits Computers Fault tolerance Hadamard matrix Hard problems Humanities and Social Sciences Methods multidisciplinary Optimization algorithms QAOA Quantum annealing Quantum approximate optimization algorithm Quantum computing Science Science (multidisciplinary) Hadamard matrix Noisy Intermediate-Scale Quantum (NISQ) Quantum computing Quantum advantage Hard problems Utility-Scale Quantum Computing QAOA Quantum annealing Quantum Optimization Quantum approximate optimization algorithm
ISSN:	2045-2322, 2045-2322
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Abstract	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 . 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.
AbstractList	Abstract 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. 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 . 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. 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 . 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. 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 [Formula: see text]. 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. 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 [Formula: see text]. 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.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 [Formula: see text]. 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.
ArticleNumber	33254
Author	Suksmono, Andriyan Bayu
Author_xml	– sequence: 1 givenname: Andriyan Bayu surname: Suksmono fullname: Suksmono, Andriyan Bayu email: suksmono@itb.ac.id organization: The School of Electrical Engineering and Informatics, Institut Teknologi Bandung, ITB Research Center on ICT (PPTIK-ITB), Institut Teknologi Bandung (ITB), University Center of Excellence for Space Science, Technology, and Innovation (PSTIA-ITB), Institut Teknologi Bandung, Research Collaboration Center for Quantum Technology 2.0, BRIN-ITB-Telkom University
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Keywords	Hadamard matrix Noisy Intermediate-Scale Quantum (NISQ) Quantum computing Quantum advantage Hard problems Utility-Scale Quantum Computing QAOA Quantum annealing Quantum Optimization Quantum approximate optimization algorithm
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Snippet	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... Abstract Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts...
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SubjectTerms	639/166/987 639/766/483/481 Algorithms Approximation Boolean Circuits Computers Fault tolerance Hadamard matrix Hard problems Humanities and Social Sciences Methods multidisciplinary Optimization algorithms QAOA Quantum annealing Quantum approximate optimization algorithm Quantum computing Science Science (multidisciplinary)
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Title	A quantum approximate optimization method for finding Hadamard matrices
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