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arXiv · 2202.01735

Universal Statistical Simulator

Mark Carney·Ben Varcoe
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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.

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Mark Carney, Ben Varcoe. 2022-02-03. Universal Statistical Simulator. https://arxiv.org/abs/2202.01735

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