Answering Counting Queries with Differential Privacy on a Quantum Computer
Arghya Mukherjee, Hassan Jameel Asghar, Gavin K. Brennen
Abstract
Differential privacy is a mathematical notion of data privacy that has fast become the de facto standard in privacy-preserving data analysis. Recently a lot of work has focused on differential privacy in the quantum setting. Continuing on this line of study, we investigate how to answer counting queries on a quantum encoded dataset with differential privacy. An example of a counting query is ``How many people in the dataset are over the age of 25 and with a university education?'' Counting queries form the most basic but nonetheless rich set of statistics extractable from a dataset. We show that answering these queries on a quantum encoded dataset reduces to measuring the amplitude of one of two orthogonal states. We then analyze the differential privacy properties of two algorithms from literature to measure amplitude: one which performs repeated measurements in the computational basis, and the other which utilizes the classic amplitude estimation algorithm. For the first technique, we prove privacy results for the case of counting queries that improve on previously known results on general queries, and show that the mechanism in fact \emph{amplifies} privacy due to inherent randomness. For the second method, we derive a tight bound on maximum possible change in the amplitude if we add or remove a single item in the dataset, a quantity called global sensitivity which is central in making an algorithm differentially private. We then show a differentially private version of the amplitude estimation algorithm for counting queries. We also discuss how these methods can be outsourced to a quantum server to blindly compute counting queries with differential privacy.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper addresses the problem of answering counting (predicate) queries with differential privacy on quantum-encoded datasets. The main contributions are threefold:
1. Refined privacy analysis for direct measurement: The authors show that repeatedly measuring a quantum-encoded dataset to answer counting queries yields stronger privacy guarantees than previously established for generic queries in [Angrisani et al., 2022]. They exploit the structure of counting queries (global sensitivity = 1/n) and the inherent randomness of quantum measurement to demonstrate a spectrum of (ε'_k, δ_k)-DP guarantees, including the notable special case k=0 where differential privacy is achieved *without* adding explicit noise.
2. Global sensitivity of the amplitude estimation angle: The paper derives a tight bound on |θ_α - θ_α'| ≤ sin⁻¹(1/√n) when neighboring datasets differ by 1/n in query answer, enabling the application of the Laplace mechanism to the phase parameter in canonical amplitude estimation. This is proven through a careful mathematical argument leveraging concavity of sin²x on [π/4, π/2].
3. A differentially private amplitude estimation algorithm: They design a unitary operator U_η that adds calibrated Laplace noise to the eigenvalue phase before measurement, creating a DP version of Brassard et al.'s amplitude estimation algorithm.
Methodological Rigor
The mathematical treatment is generally sound and detailed. The proof of Theorem 8 (global sensitivity of the angle) is the most technically involved contribution, built through a sequence of lemmas exploiting the concavity of sin²x and the Mean Value Theorem. The argument is complete, covering all cases (both angles in [π/4, π/2], both in [0, π/4], and the mixed case).
The privacy analysis in Theorem 6 via Algorithm 1 is elegant—the observation that measuring the quantum state is equivalent to uniform sampling from the dataset with replacement is key. The binomial distribution over the number of times the differing row is sampled creates a natural privacy amplification effect. This is conceptually clean and well-executed.
However, there are some concerns:
Potential Impact
The paper sits at the intersection of quantum computing and differential privacy, a growing but still niche area. The practical impact is currently limited by:
The theoretical contributions—particularly the global sensitivity analysis of the angle parameter and the privacy amplification through measurement—could influence future work on quantum private data analysis. The sensitivity result (Corollary 1) is clean and could be reused in other quantum DP contexts involving amplitude estimation.
The blind computation discussion (Section 5) adds practical relevance but remains at a high level, with significant client interaction needed for non-Clifford gates.
Timeliness & Relevance
The paper addresses a timely topic. Quantum differential privacy has seen increasing attention (Zhou & Ying 2017, Aaronson & Rothblum 2019, Angrisani et al. 2022-2025). Counting queries are fundamental in data analysis and census applications, making this a natural problem to study. However, the practical relevance is somewhat ahead of its time given the current state of quantum hardware.
Strengths
1. Clear problem formulation: The reduction of counting queries to amplitude measurement (Eq. 4-5) is clean and provides a nice framework.
2. Tight sensitivity bound: Theorem 8 provides a tight characterization that is mathematically satisfying and practically useful.
3. Spectrum of privacy guarantees: The k-parameterized family of (ε'_k, δ_k)-DP guarantees offers flexibility for practitioners.
4. Concrete numerical examples: The paper provides specific parameter calculations (e.g., n=10⁶, t=10³) that ground the theoretical results.
5. Comprehensive treatment: Including depolarizing noise analysis and homomorphic encryption discussion gives a complete picture.
Limitations
1. Novelty concerns: The equivalence to classical subsampling (Algorithm 1) weakens the claim of quantum advantage. The privacy amplification in the direct measurement case is essentially a known phenomenon (subsampling amplification) in quantum dress.
2. Limited experimental validation: No simulations or implementations are provided to demonstrate practical utility.
3. Scalability questions: The O(mn) state preparation cost and requirement for fresh copies per measurement in the direct method raise scalability concerns.
4. Narrow query class: Only predicate/counting queries are considered; extension to more complex statistical queries is left as future work.
5. Error in prior work: The noted error in [3] (Table 1) raises questions about whether the comparison baseline is correctly stated.
6. The amplitude estimation DP mechanism adds noise before measurement via a specially constructed unitary, but the practical implementation of sampling η from a Laplace distribution and constructing U_η on a quantum computer is non-trivial and not fully addressed.
Overall Assessment
This is a technically competent paper that makes incremental but meaningful contributions to quantum differential privacy. The sensitivity analysis for amplitude estimation is the strongest technical result. The privacy amplification analysis, while well-executed, is somewhat less novel given its equivalence to classical subsampling. The paper would benefit from experimental validation and a clearer articulation of when quantum approaches genuinely outperform classical ones for this problem.
Generated Apr 14, 2026
Comparison History (85)
Paper 1 addresses a critical bottleneck in scalable quantum computing—mapping fault-tolerant surface codes onto realistic silicon spin-qubit architectures with shuttling. It provides concrete threshold analyses, demonstrates that noise-bias-aware code selection (XZZX) yields substantial hardware reductions, and charts a practical pathway to early fault-tolerant processors. This directly impacts the rapidly advancing field of quantum hardware engineering. Paper 2, while interesting, addresses a more niche intersection of differential privacy and quantum computing with limited near-term practical relevance, as quantum-encoded datasets are far from realization.
Paper 2 has higher impact potential: it advances differential privacy in the quantum setting with concrete algorithms (including a DP variant of amplitude estimation), improved privacy bounds for counting queries, and an outsourcing/blind-computation angle—connecting theory to likely real-world applications in privacy-preserving quantum data analytics and cloud quantum services. Its contributions are timely given active interest in quantum computing and privacy. Paper 1 is conceptually rigorous and clarifies limits of local hidden-variable dynamics, but is more specialized/foundational with narrower immediate applications and less cross-disciplinary uptake outside quantum foundations.
Paper 2 addresses the intersection of two high-impact fields—quantum computing and differential privacy—with broad applicability to data privacy, a critical societal concern. It provides novel theoretical contributions (tight bounds on global sensitivity, privacy amplification results) and practical implications for outsourcing private computation to quantum servers. Paper 1, while methodologically sound, applies quantum walks to protein networks with results that largely agree with classical eigenvector centrality, limiting its novelty. The quantum advantage demonstrated is incremental, and the biological validation is limited to two proteins. Paper 2's broader relevance to data science and privacy gives it higher cross-disciplinary impact potential.
Paper 1 bridges two highly active and impactful fields: differential privacy and quantum computing. It addresses a fundamental problem (secure counting queries) with clear, near-term real-world applications in privacy-preserving data analysis and secure quantum cloud computing. Paper 2, while mathematically rigorous and theoretically profound, focuses on deep algebraic structures in quantum field theory, which generally has a narrower, more specialized audience and longer path to practical application.
Paper 2 merges quantum computing with differential privacy, addressing a critical real-world challenge in secure data analysis and cloud computing. Its implications for privacy-preserving quantum databases give it broader interdisciplinary appeal and higher practical application potential than Paper 1. While Paper 1 presents an innovative ML approach to quantum metrology, its explicitly stated scalability limits (restricting it to 6 qubits due to operator space growth) constrain its immediate broader impact compared to the foundational privacy algorithms developed in Paper 2.
Paper 1 bridges quantum computing and differential privacy, two rapidly growing fields with massive implications for secure data analysis. Its focus on fundamental dataset operations (counting queries) suggests broad applicability across computer science, cryptography, and data science. Paper 2, while methodologically rigorous and valuable for precision sensing, is more narrowly focused on trapped-ion physics and phonon lasing, resulting in a more specialized, narrower scope of impact compared to the highly interdisciplinary reach of Paper 1.
Paper 2 establishes a unified theoretical framework for the Mpemba effect in quantum imaginary-time evolution, providing necessary and sufficient conditions for a counterintuitive phenomenon with direct practical implications for quantum state preparation efficiency. This addresses a fundamental bottleneck in quantum computing (reducing evolution duration for ground/thermal state preparation). Paper 1, while solid, addresses a more incremental contribution at the intersection of differential privacy and quantum computing for counting queries—a narrower niche. Paper 2's broader relevance to quantum simulation, state preparation, and non-equilibrium dynamics gives it wider cross-field impact.
Paper 2 addresses a concrete physical platform (molecular optomechanical cavities) for infrared-to-visible frequency upconversion with practical implications for sensing and detection technologies. It builds on demonstrated amplification mechanisms and provides rigorous noise analysis approaching quantum limits. Paper 1, while technically solid, operates at the intersection of two fields (quantum computing and differential privacy) where practical quantum advantages remain distant. Paper 2's results are more immediately applicable to experimental physics and photonics, with broader near-term impact across quantum sensing, spectroscopy, and communications.
Paper 1 bridges two highly active and critical fields: quantum computing and differential privacy. By focusing on fundamental counting queries and providing algorithms for privacy-preserving data analysis on quantum servers, it offers significant potential for real-world applications in secure quantum cloud computing. Paper 2 presents a valuable methodological transfer for fundamental physics, but Paper 1 has broader cross-disciplinary appeal and more immediate implications for future technological infrastructure.
Paper 2 addresses a critical and immediate bottleneck in quantum computing—circuit depth and hardware decoherence—by reducing circuit complexity from O(n^2) to O(n log n) or O(n). This practical optimization enables near-term quantum devices to simulate complex physical systems like fluid dynamics, offering broad applications across physics and engineering. Paper 1 is highly innovative but relies on the assumption of quantum-encoded datasets and servers, which are further from practical realization. Paper 2's direct impact on making quantum simulations viable on NISQ-era devices gives it a higher potential scientific impact.
Paper 2 is likely to have higher impact due to broader cross-field relevance (privacy, learning theory, quantum algorithms, cryptography) and strong real-world applicability as quantum data processing emerges. It provides theoretical advances: tighter privacy guarantees for counting queries, privacy amplification via measurement randomness, sensitivity bounds, and a differentially private amplitude-estimation variant, plus an outsourcing/blind-computation angle. Paper 1 is a valuable, timely benchmark for multistate quantum chemistry ansätze, but its impact is narrower (surface chemistry/quantum simulation) and more contingent on near-term hardware feasibility and domain-specific uptake.
Paper 2 addresses a deep foundational question connecting black hole physics with quantum foundations (Wigner's Friend paradoxes), two of the most active areas in theoretical physics. Its interdisciplinary nature bridging quantum gravity and quantum foundations, combined with its engagement with high-profile recent work (Hausmann-Renner), gives it broader impact potential. It proposes substantive philosophical conclusions (intrinsic relationality, retrocausality) that could influence multiple research programs. Paper 1, while technically sound, addresses a more niche intersection of quantum computing and differential privacy with incremental improvements on existing results.
Paper 2 likely has higher impact due to strong real-world applicability and breadth: improving fermion-to-qubit mappings directly reduces resource overhead for quantum simulation across condensed matter and chemistry, a core near-term quantum computing workload. It proposes a scalable optimization framework with extensive benchmarking (large Hubbard lattices, molecular Hamiltonians with many Pauli terms), suggesting methodological maturity and immediate utility. Paper 1 is novel at the intersection of quantum algorithms and differential privacy, but its applicability depends on less-common “quantum-encoded datasets” and hinges on practical deployment of quantum data/servers, making near-term uptake narrower despite solid theoretical contributions.
Paper 1 bridges quantum computing and differential privacy, two highly active and rapidly growing fields. Its focus on privacy-preserving data analysis has clear, broad real-world applications across data science, cryptography, and quantum computing. While Paper 2 presents interesting foundational physics regarding time crystals, Paper 1 has higher potential for interdisciplinary impact and immediate practical relevance in secure quantum data processing.
Paper 2 combines two rapidly growing and highly impactful fields: quantum computing and differential privacy. Its focus on answering counting queries securely on quantum datasets has broad, real-world applications in secure cloud computing and privacy-preserving data analysis across multiple disciplines. While Paper 1 provides a rigorous theoretical critique valuable to quantum chemistry, Paper 2's cross-disciplinary approach and high relevance to modern data security give it a greater potential for widespread scientific and technological impact.
Paper 1 offers a more novel, theory-driven contribution at the intersection of quantum algorithms and differential privacy: it derives improved privacy guarantees for quantum measurement-based mechanisms, provides tight global sensitivity bounds for quantum amplitude estimation on counting queries, and proposes a differentially private amplitude-estimation variant with potential for outsourced/blind quantum computation. These results are broadly relevant to privacy-preserving data analysis and quantum information. Paper 2 is timely and practically motivated, but largely constitutes a benchmarking study of known noise-mitigation techniques on small HQNN examples with limited methodological novelty and narrower generalization.
Paper 1 presents a fundamental theoretical advance in quantum thermometry by demonstrating that non-completely positive encoding maps arising from initial probe-environment correlations can surpass previously established precision bounds. This challenges conventional assumptions in quantum metrology and opens new avenues for enhanced quantum sensing. Paper 2 addresses an interesting intersection of differential privacy and quantum computing for counting queries, but is more incremental—applying known techniques (amplitude estimation, differential privacy) to a specific problem. Paper 1's impact is broader, affecting foundational quantum metrology and thermodynamics, while Paper 2 has narrower applicability in a still-nascent field.
Paper 1 presents a concrete, first-of-its-kind experimental breakthrough with immediate and broad applications in 3D quantum sensing and imaging, impacting fields like biology, medicine, and materials science. Paper 2 is highly innovative in combining differential privacy with quantum computing, but its impact is currently constrained by the theoretical nature of large-scale quantum data processing. Thus, Paper 1 promises higher near-term and interdisciplinary scientific impact.
Paper 1 combines two highly relevant and rapidly growing fields: differential privacy and quantum computing. Its focus on answering counting queries offers clear, practical real-world applications for privacy-preserving data analysis and secure quantum server outsourcing. While Paper 2 provides important theoretical insights into quantum correlations under complexity constraints, Paper 1 has broader cross-disciplinary appeal and greater potential for immediate real-world technological impact.
Paper 1 bridges quantum computing and differential privacy, two highly relevant and rapidly growing fields. By providing concrete mechanisms for differentially private counting queries, it offers clear potential for real-world applications in secure data analysis and quantum cloud computing. While Paper 2 presents profound theoretical insights into quantum information and complexity, Paper 1's cross-disciplinary appeal, practical utility, and timeliness give it a higher potential for broad scientific and societal impact.