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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Bibliographic Details
Published in:Scientific reports Vol. 15; no. 1; pp. 33254 - 16
Main Author: Suksmono, Andriyan Bayu
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 26.09.2025
Nature Publishing Group
Nature Portfolio
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-025-18778-1