Abstract
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.
Highlights
A Hadamard matrix (H-matrix) is a binary orthogonal matrix with {−1, +1} elements whose any distinct pair of its columns are orthogonal to each other
We have proposed to find such a matrix by using a quantum computer considering its capability in solving hard problems17
We show that by adopting the classical searching methods, we can reduce the required computing resource, which for a quantum annealing processor implementing the Ising model, will become O(M2)
Summary
A Hadamard matrix (H-matrix) is a binary orthogonal matrix with {−1, +1} elements whose any distinct pair of its columns (or rows) are orthogonal to each other. We show that by adopting the classical searching methods, we can reduce the required computing resource, which for a quantum annealing processor implementing the Ising model, will become O(M2) .
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