A Note on Enumeration by Fair Sampling

TL;DR

This paper presents an improved algorithm for enumerating all elements of a finite set using fair sampling, applicable to quantum annealing, with mathematical analysis and numerical validation.

Contribution

It introduces a new enumeration algorithm based on coupon collector's lemma, enhancing previous methods for fair sampling in quantum annealing.

Findings

Algorithm effectively enumerates set elements using uniform sampling.

Mathematical analysis confirms efficiency improvements.

Numerical demonstrations validate practical applicability.

Abstract

This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on a lemma of the coupon collector's problem and is an improved version of the algorithm described in arXiv:2007.08487 (2020). We provide a mathematical analysis and a numerical demonstration of our algorithm.