Finding Hadamard Matrices Using Quantum Computers

Speaker:  Andriyan Bayu Suksmono – Bandung, Indonesia
Topic(s):  Computational Theory, Algorithms and Mathematics , Applied Computing

Abstract

Quantum computing — harnessing the superposition, tunneling, and entanglement principles — offers capabilities of problem solving beyond the classical Turing-Machine mode. This presentation summarizes four approaches for finding Hadamard matrices (QHSA-Quantum Hadamard matrix Search Algorithm), quantum algorithms developed by the speaker since 2017 which are published in a series of papers. The first approach (QHSA-1, the direct method) successfully identifies small Hadamard matrices but is inefficient due to its complexity, and when implemented on a quantum annealer it requires ancillary qubits, increasing the complexity. The second approach (QHSA-2) adopts classical search techniques, theoretically reducing the complexity significantly, but its implementation on a quantum annealer remains inefficient because ancillary qubits raise the complexity. The third approach (QHSA-3) applies classical search methods to a gate-based quantum computer using QAOA and is the most resource-efficient, requiring fewer quantum resources; and like the previous two, it is optimization-based. The fourth approach (QHSA-4) differs fundamentally by employing an oracle to test orthogonality followed by probability-amplitude amplification via Grover’s algorithm, making it a non-optimization method. These studies provide complementary pathways — both optimization and oracle-driven — toward harnessing quantum computing to solve the Hadamard matrix search problem as a promising candidate for near-term demonstrations of practical quantum advantage.

About this Lecture

Number of Slides:  50
Duration:  45 minutes
Languages Available:  English
Last Updated:  03/12/2025

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