Matrix algebra: Quantum computer

As we know, the quantum Fourier transform (QFT) allows us to efficiently add and multiply any two given numbers on a quantum computer or PennyLane simulator. Recently, I’ve been contemplating how I could extend this concept to perform addition and multiplication operations on matrices, particularly non-identity matrices of 2-by-2 or higher order. I’m curious about the types of circuits and quantum information that would be required for such operations.

Any assistance or insights on this matter would be greatly appreciated.

Best wishes!

Hello @rkja!

Although I’m not sure how we could use QFT specifically for matrix operations, there are some known quantum algorithms that can perform some matrix operations. For example, the linear combination of unitaries can add unitary matrices. And the Quantum Singular Value Transform can aid in the calculation of matrix polynomials. These topics may serve as inspiration to do further research in this area.