Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum...

Area of Science:

• Quantum Computing
• Computational Mathematics
• Matrix Theory

Background:

• Finding Hadamard matrices (H-matrices) is computationally challenging.
• Previous quantum methods were limited to low-order H-matrices (orders 2 and 4).

Purpose of the Study:

• To develop novel quantum computing methods for discovering higher-order H-matrices.
• To leverage classical searching techniques within quantum algorithms.

Main Methods:

• Formulating new quantum computing approaches by integrating classical search strategies.
• Implementing a classical-quantum resource balancing method.

Main Results:

• Successfully found H-matrices of order exceeding one hundred.
• Reproduced a 92-order H-matrix discovery using a classical-quantum approach, matching a 1961 mainframe result.
• Solutions are verifiable via polynomial-time orthogonality tests.

Conclusions:

• The proposed method significantly advances the search for high-order H-matrices.
• This approach shows potential for demonstrating practical quantum supremacy due to efficient solution verification.