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arXiv:2506.07724 · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)

Optimal quantum sampling on distributed databases

Longyun Chen, Jingcheng Liu, Penghui Yao

Published Jul 16, 2025• 0 citations
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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.

DOI
10.1145/3694906.3743335

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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.
We present a novel quantum communication protocol for "Private Data Sampling", where a player (Bob) obtains a random sample of limited size of a classical database, while the database owner (Alice) remains oblivious as to which bits were accessed. The protocol is efficient in the sense that the communication complexity per query scales at most linearly with the size of the database. It does not violate Lo's "no-go" theorem for one-sided twoparty secure computation, since a given joint input by Alice and Bob can result in randomly different protocol outcomes. After outlining the main security features of the protocol, we present our first experimental results.
Quantum computing represents a next-generation technology in data processing, promising to transcend the limitations of traditional computation. In this paper, we undertake an early exploration of the potential integration of quantum computing with database query optimization. We introduce a pioneering hybrid classical-quantum algorithm for sampling-based approximate query processing (AQP). The core concept of the algorithm revolves around identifying rare groups, which often follow a long-tail distribution, and applying distinct sampling methodologies to normal and rare groups. By leveraging the quantum capabilities of the diffusion gate and QRAM, the algorithm defines a novel quantum sampling approach that iteratively amplifies the signals of these infrequent groups. The algorithm operates without the need for preprocessing or prior knowledge of workloads or data. It utilizes the power of quadratic acceleration to achieve well-balanced sampling across various data categories. Experimental results demonstrate that in the context of AQP, the new sampling scheme provides higher accuracy at the same sampling cost. Additionally, the benefits of quantum computing become more pronounced as query selectivity increases.
This paper presents a novel distributed quantum state framework designed to facilitate large-scale quantum computation by leveraging the inherent parallelism and storage capabilities of quantum states. Traditional quantum computing relies on the computation of a single qubit, limiting scalability. This framework employs a distributed architecture, allowing for the concurrent processing of multiple quantum states, drastically reducing the computational burden and enabling more efficient execution of complex algorithms. The core mechanism focuses on establishing and managing a quantum state database across multiple nodes, enabling parallel computations and optimizing resource utilization. We explore the design and implementation of key components, including state partitioning, error mitigation strategies, and a communication protocol optimized for distributed data exchange. The paper concludes with a discussion of the potential benefits and challenges of this approach in advancing the field of quantum computing.
Aaronson and Ambainis (Theory of Computing, 2014) conjectured that quantum query algorithms admit efficient almost-everywhere classical simulation: for any TTT-query quantum algorithm, its acceptance probability can be approximated on a (1−δ)(1-δ)(1−δ) fraction of inputs, up to εεε additive error, using poly(T,1/ε,1/δ)\mathrm{poly}(T, 1/ε, 1/δ)poly(T,1/ε,1/δ) classical queries. At a high level, the conjecture suggests that exponential quantum speedups are possible only on sufficiently structured inputs. In this work, we make progress on this conjecture by proving it for quantum algorithms that make massively parallel quantum queries. In contrast, Yamakawa and Zhandry (Journal of the ACM, 2024) showed that quantum algorithms restricted to parallel queries can still achieve exponential speedups over classical algorithms for sampling problems. We establish our simulation theorem by proving the stronger statement that parallel-query quantum algorithms cannot distinguish the uniform distribution over oracles from oracles drawn from so-called "dense distributions". Our main technical contribution is a coupling theorem that relates the uniform distribution over oracles to oracles drawn from dense distributions. We further extend this approach beyond the purely parallel setting. We prove simulation theorems for quantum algorithms with constant rounds of adaptivity, and for quantum algorithms with a bounded quantum-query prefix followed by a massively parallel quantum-query stage.
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We introduce a "statistical query sampling" model, in which the goal of an algorithm is to produce an element in a hidden set S/spl sube/{0,1}/sup n/ with reasonable probability. The algorithm gains information about S through oracle calls (statistical queries), where the algorithm submits a query function g(/spl middot/) and receives an approximation to Pr/sub x/spl isin/S/[g(x)=1]. We show how this model is related to NMR quantum computing, in which only statistical properties of an ensemble of quantum systems can be measured, and in particular to the question of whether one can translate standard quantum algorithms to the NMR setting without putting all of their classical postprocessing into the quantum system. Using Fourier analysis techniques developed in the related context of statistical query learning, we prove a number of lower bounds (both information-theoretic and cryptographic) on the ability of algorithms to produce an x/spl isin/S, even when the set S is fairly simple. These lower bounds point out a difficulty in efficiently applying NMR quantum computing to algorithms such as Shor's and Simon's algorithm that involve significant classical postprocessing. We also explicitly relate the notion of statistical query sampling to that of statistical query learning.