Rapid sampling through quantum computing

TL;DR

This paper introduces a quantum algorithm that efficiently creates specific superpositions and samples from arbitrary probability distributions in O(√N) steps, outperforming classical methods.

Contribution

It extends quantum search algorithms to multiple solutions, enabling rapid superposition creation and sampling from arbitrary distributions.

Findings

Quantum superpositions can be created in O(√N) steps.

Sampling from arbitrary distributions is achievable in O(√N) steps.

Classical algorithms require O(N) steps for similar tasks.

Abstract

This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space. This yields new applications - an algorithm is presented that can create an arbitrarily specified quantum superposition on a space of size N in O(sqrt(N)) steps. By making a measurement on this superposition, it is possible to obtain a sample according to an arbitrarily specified classical probability distribution in O(sqrt(N)) steps. A classical algorithm would need O(N) steps.