The problem of computing symmetric Hadamard matrices of the Balonin-Siberry construction is considered. To obtain such matrices, a large number of random binary sequences are required to select three of them, which are bound by the requirements of the matrix design. Such sequences are the first rows of three cyclic blocks of Hadamard matrices. The background of the emergence of quantum computing and the advantage of quantum generation of binary sequences for subsequent selection are considered. The calculation of Hadamard matrices is proposed as a test problem for quantum computers, which allows to show quantum superiority.

Keywords: quantum computers, qubits, random number generators, orthogonal matrices, Mersenne matrices, Kronecker product