Universal Statistical Simulator

• URL: http://arxiv.org/abs/2202.01735v1
• Date: Thu, 3 Feb 2022 17:55:58 GMT
• Title: Universal Statistical Simulator
• Authors: Mark Carney, Ben Varcoe
• Abstract summary: We present a quantum computer code for a Galton Board Simulator that is exponentially faster than a classical calculation. We demonstrate a straight forward implementation on a quantum computer, using only three types of quantum gate, which calculates $2n$ trajectories using $mathcalO (n2)$ resources.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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