Determining probability density functions with adiabatic quantum computing

TL;DR

This paper introduces a hybrid quantum computing method combining analog and gate-based approaches to fit probability distributions, specifically by encoding data in adiabatic evolution and translating it into quantum circuits for density estimation.

Contribution

It presents a novel strategy for encoding and fitting probability distributions using adiabatic quantum computing combined with circuit translation techniques.

Findings

Successfully encodes data within adiabatic evolution

Translates adiabatic process into quantum circuit for density estimation

Enables computation of probability density via parameter shift rules

Abstract

The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a method for fitting one-dimensional probability distributions as a practical example of how analog and gate-based computation can be used together to perform different tasks within a single algorithm. In particular, we propose a strategy for encoding data within an adiabatic evolution model, which accomodates the fitting of strictly monotonic functions, as it is the cumulative distribution function of a dataset. Subsequently, we use a Trotter-bounded procedure to translate the adiabatic evolution into a quantum circuit in which the evolution time t is identified with the parameters of the circuit. This facilitates computing the probability density as derivative of the cumulative function using parameter shift rules.