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

TL;DR

This paper introduces a hybrid classical-quantum method for efficiently preparing bell-shaped probability distributions on quantum hardware by using deconvolution techniques to reduce circuit complexity and enable parallel processing.

Contribution

It presents a novel deconvolution-based approach for quantum state preparation that reduces circuit depth and facilitates parallel data loading of bell-shaped distributions.

Findings

Successfully loaded normal and Laplace distributions on IBM quantum hardware.

Reduced quantum circuit depth through deconvolution and parallel processing.

Validated approach on IBMQ Kolkata with 27-qubit processor.

Abstract

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.