Loading Probability Distributions in a Quantum circuit

TL;DR

This paper explores methods to construct parameterized quantum circuits capable of generating various probability distributions, including symmetric and asymmetric ones, using variational optimization and testing on simulators and IBM hardware.

Contribution

It introduces a systematic approach to design quantum circuits for generating specific probability distributions, advancing applications in finance and physics.

Findings

Successful generation of symmetric and asymmetric distributions

Effective variational optimization of circuit parameters

Validation on both simulators and real quantum hardware

Abstract

Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require circuits that can initialize the wave function of a physical quantum system. These wave functions, in several cases, are identical to some very well known probability distributions. In this paper we discuss ways to construct parameterized quantum circuits that can generate both symmetric as well as asymmetric distributions. We follow the trajectory of quantum states as single and two qubit operations get applied to the system, and find out the best possible way to arrive at the desired distribution. The parameters are optimized by a variational solver. We present results from both simulators as well as real IBM quantum hardwares.