How to Teach a Quantum Computer a Probability Distribution

TL;DR

This paper investigates methods to teach a quantum walk on a regular graph to produce specific probability distributions by tuning angles and Lie algebra parameters, with implications for quantum algorithms and machine learning.

Contribution

It introduces two novel parameter adjustment techniques for quantum walks to achieve desired distributions, expanding their potential applications.

Findings

Parameter tuning effectively shapes quantum walk distributions

Connections to machine learning suggest new algorithmic applications

Discussion of hardware and software considerations for implementation

Abstract

Currently there are three major paradigms of quantum computation, the gate model, annealing, and walks on graphs. The gate model and quantum walks on graphs are universal computation models, while annealing plays within a specific subset of scientific and numerical computations. Quantum walks on graphs have, however, not received such widespread attention and thus the door is wide open for new applications and algorithms to emerge. In this paper we explore teaching a coined discrete time quantum walk on a regular graph a probability distribution. We go through this exercise in two ways. First we adjust the angles in the maximal torus $\mathbb{T}^d$ where $d$ is the regularity of the graph. Second, we adjust the parameters of the basis of the Lie algebra $\mathfrak{su}(d)$. We also discuss some hardware and software concerns as well as immediate applications and the several connections to machine learning.