One of the applications of quantum computers is to create, store, manipulate and interrogate multivariate functions, in what we can call "quantum numerical analysis". This talk explains two approaches to this field. In the first half, I discuss how machine learning ideas can be brought into the quantum world, to create quantum neural networks and approximate arbitrary functions. In the second part, I discuss how smooth, bandwidth limited functions can be encoded using a finite number of qubits, to implement interpolation, Fourier analysis, and solving partial derivative equations. As spin-off of this idea, I will discuss how those algorithms can not only be implemented in quantum computers but, in some cases, also using tensor network states.
Bibliography
[1] Torrontegui, E. and García-Ripoll, J.J., 2019. Unitary quantum perceptron as efficient universal approximator. EPL (Europhysics Letters), 125(3), p.30004
[2] García-Ripoll, J.J., 2019. Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations. arXiv preprint arXiv:1909.06619
