Quantum state preparation for bell-shaped probability distributions
  using deconvolution methods
Quantum systems are a natural choice for generating probability distributions
due to the phenomena of quantum measurements. The data that we observe in
nature from various physical phenomena can be modelled using quantum circuits.
To load this data, which is mostly in the form of a probability distribution,
we present a hybrid classical-quantum approach. The classical pre-processing
step is based on the concept of deconvolution of discrete signals. We use the
Jensen-Shannon distance as the cost function to quantify the closeness of the
outcome from the classical step and the target distribution. The chosen cost
function is symmetric and allows us to perform the deconvolution step using any
appropriate optimization algorithm. The output from the deconvolution step is
used to construct the quantum circuit required to load the given probability
distribution, leading to an overall reduction in circuit depth. The
deconvolution step splits a bell-shaped probability mass function into smaller
probability mass functions, and this paves the way for parallel data processing
in quantum hardware, which consists of a quantum adder circuit as the
penultimate step before measurement. We tested the algorithm on IBM Quantum
simulators and on the IBMQ Kolkata quantum computer, having a 27-qubit quantum
processor. We validated the hybrid Classical-Quantum algorithm by loading two
different distributions of bell shape. Specifically, we loaded 7 and 15-element
PMF for (i) Standard Normal distribution and (ii) Laplace distribution.
Kiratholly Nandakumar Madhav Sharma Camille de Valk Ankur Raina Julian van Velzen