This paper introduces an innovative and practical approach to universal quantum matrix multiplication. We designed optimized quantum adders and multipliers based on Quantum Fourier Transform (QFT), which significantly reduced the number of gates used compared to classical adders and multipliers. Subsequently, we construct a basic universal quantum matrix multiplication and extend it to the Strassen algorithm. We conduct comparative experiments to analyze the performance of the quantum matrix multiplication and evaluate the acceleration provided by the optimized quantum adder and multiplier. Furthermore, we investigate the advantages and disadvantages of the quantum Strassen algorithm compared to basic quantum matrix multiplication.

This article gives an overview and a perspective of recent theoretical proposals and their experimental implementations in the field of quantum machine learning. Without an aim to being exhaustive, the article reviews specific high-impact topics such as quantum reinforcement learning, quantum autoencoders, and quantum memristors, and their experimental realizations in the platforms of quantum photonics and superconducting circuits. The field of quantum machine learning could be among the first quantum technologies producing results that are beneficial for industry and, in turn, to society. Therefore, it is necessary to push forward initial quantum implementations of this technology, in Noisy Intermediate-Scale Quantum Computers, aiming for achieving fruitful calculations in machine learning that are better than with any other current or future computing paradigm.

Recently, it was proposed to employ approximate quantum adders to implement quantum autoencoders in quantum technologies. Here, we carry out the experimental implementation of this proposal in the Rigetti cloud quantum computer employing up to three qubits. The experimental fidelities are in good agreement with the theoretical prediction, thus proving the feasibility to realize quantum autoencoders via quantum adders in state-of-the-art superconducting quantum technologies. A quantum autoencoder is a quantum device which can reshuffle and compress the quantum information of a subset of a Hilbert space spanned by initial n -qubit states onto n ′ qubit states with n ′ n [1, 2]. This approach may allow one to employ fewer quantum computing resources [3, 4]. On the other hand, recently it was proven that a general quantum adder performing the equal weight superposition of two unknown quantum states is forbidden in general [5].