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Quantum systems are a natural choice for generating probability distributionsdue to the phenomena of quantum measurements. The data that we observe innature from various physical phenomena can be modelled using quantum circuits.We present a hybrid approach to loading probability distributions by performingdeconvolution as a pre-processing step before the quantum circuit. To quantifythe closeness of the distribution of outcomes from the hybrid classical-quantumblock and the target distribution, we use the Jensen-Shannon distance as thecost function. The chosen cost function is symmetric and allows us to improvethe deconvolution step before the use of quantum circuits leading to an overallreduction of the circuit depth. The deconvolution step consists of splitting abell-shaped probability mass function into smaller probability mass functions.The classical step paves the way for parallel data processing in the quantumhardware that consists of a quantum adder circuit as the penultimate stepbefore measurement. We test the algorithm on IBM Quantum simulators and IBMQKolkata, a 27-qubit quantum processor, and validate the hybridClassical-Quantum algorithm by loading two different distributions of bellshape. We load 7 and 15-element PMF of (i) Standard Normal distribution and(ii) Laplace distribution.

Quantum state preparation for bell-shaped probability distributions using deconvolution methods