Universal Statistical Simulator

TL;DR

This paper introduces a quantum algorithm for a Galton Board simulator that is exponentially faster than classical methods, with a simple implementation and potential for universal statistical simulation.

Contribution

It presents a quantum circuit for a Galton Board that is resource-efficient, has lower depth, and can be extended to a universal statistical simulator by modifying its structure.

Findings

Quantum Galton Board simulator computes $2^n$ trajectories with $ ext{O}(n^2)$ resources.

The circuit has lower depth than previous quantum implementations.

The approach can be extended to a universal statistical simulator by structural modifications.

Abstract

The Quantum Fourier Transform is a famous example in quantum computing for being the first demonstration of a useful algorithm in which a quantum computer is exponentially faster than a classical computer. However when giving an explanation of the speed up, understanding computational complexity of a classical calculation has to be taken on faith. Moreover, the explanation also comes with the caveat that the current classical calculations might be improved. In this paper we present a quantum computer code for a Galton Board Simulator that is exponentially faster than a classical calculation using an example that can be intuitively understood without requiring an understanding of computational complexity. We demonstrate a straight forward implementation on a quantum computer, using only three types of quantum gate, which calculates $2^n$ trajectories using $\mathcal{O} (n^2)$ resources. The circuit presented here also benefits from having a lower depth than previous Quantum Galton Boards, and in addition, we show that it can be extended to a universal statistical simulator which is achieved by removing pegs and altering the left-right ratio for each peg.