Andriyan Bayu Suksmono &amp; Yuichiro Minato January 2022 Finding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future. <a href="https://www.nature.com/articles/s41598-021-03586-0" rel="noopener noreferrer" target="_blank" style="color: rgb(34, 34, 34);">Scientific Reports</a><a href="https://arxiv.org/abs/2009.10919" rel="noopener noreferrer" target="_blank" style="color: rgb(34, 34, 34);">arXiv</a>

Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer, January 2022

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