Optimal quantum sampling on distributed databases

TL;DR

This paper explores quantum sampling in distributed databases, introducing optimal algorithms for sampling from joint data across multiple machines with minimal communication, addressing the challenge of large-scale quantum data management.

Contribution

It presents the first study of quantum sampling in a distributed setting and provides optimal sequential and parallel algorithms under the oblivious communication model.

Findings

Both algorithms are proven optimal in their respective models.

The study advances understanding of quantum sampling with distributed data.

Efficient quantum sampling reduces communication costs in distributed quantum systems.

Abstract

Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of quantum sampling in a distributed setting. Specifically, we assume that the data is distributed among multiple machines, and each machine solely maintains a basic oracle that counts the multiplicity of individual elements. Given a quantum sampling task, which is to sample from the joint database, a coordinator can make oracle queries to all machines. We focus on the oblivious communication model, where communications between the coordinator and the machines are predetermined. We present both sequential and parallel algorithms: the sequential algorithm queries the machines sequentially, while the parallel algorithm allows the coordinator to query all machines simultaneously. Furthermore, we prove that both algorithms are optimal in their respective settings.