Optimal quantum sampling on distributed databases

2025-06-09

AI Summary

This paper addresses optimal quantum sampling over distributed databases, where data is partitioned across multiple machines, each providing only a local oracle for querying the frequency of a single element; the goal is for a central coordinator to efficiently sample from the global joint distribution. Method: We establish the first theoretical framework for distributed quantum sampling and design both sequential and parallel quantum algorithms achieving optimal query complexity. Our approach leverages quantum amplitude encoding, coordinated distributed oracle queries, and quantum state preparation of probability distributions to enable exact sampling from the global distribution. Results: We rigorously prove a tight query lower bound under the oblivious communication model. Crucially, our algorithms drastically reduce reliance on large-scale quantum memory, offering the first theoretically optimal foundational subroutine for distributed quantum computing.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Study quantum sampling in distributed databases
• Optimize algorithms for sequential and parallel queries
• Prove optimality of proposed sampling algorithms

Innovation

• Distributed quantum sampling with basic oracles
• Oblivious communication model for coordination
• Optimal sequential and parallel query algorithms