Quantum Speedups for Testing Similar Means

• URL: http://arxiv.org/abs/2608.00741v1
• Date: Sat, 01 Aug 2026 16:23:28 GMT
• Title: Quantum Speedups for Testing Similar Means
• Abstract summary: This work focuses on quantum algorithms for testing whether $m$ distributions have similar means or are $$-far from mean similarity under two models.<n>In the query model, the algorithm can choose which distribution to sample from, whereas in the sampling model, the distributions are selected uniformly.
• Score: 4.1765120028423
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Property testing of distributions is a central topic in information theory, learning theory, and statistics. While quantum algorithms are known to offer significant speedups for property testing of a single distribution or a pair of distributions, it is unclear whether quantum algorithms provide speedups for property testing of $m$ ($m\geq 3$) distributions. This work focuses on quantum algorithms for testing whether $m$ distributions have similar means or are $ε$-far from mean similarity under two models. In the query model, the algorithm can choose which distribution to sample from, whereas in the sampling model, the distributions are selected uniformly. We design quantum algorithms with complexities $\tilde{O}(1/ε)$ (the $\tilde{O}$ notation hides poly-logarithmic factors) and $\tilde{O}(\sqrt{m}/ε)$ in the query and sampling models, respectively, achieving quadratic speedups over the classical counterparts. We further establish quantum lower bounds of $Ω\left(1/ε\right)$ and $Ω\rbra{m^{1/3}+\frac{m^{1/4}}ε}$ for the query model and the sampling model, demonstrating the optimality of our quantum algorithms in terms of the dependence on $ε$ up to logarithmic factors.

Related papers

• Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling [55.388363730120325]
  We parallelize the mainstream $$-leaping algorithm for absorbing discrete diffusion in a Continuous-Time Markov Chain (CTMC) framework.<n>By leveraging the continuous-time integral form of the $$-leaping algorithm and the Picard method, we achieve parallel-in-time sampling acceleration.<n>Our research expands the potential of discrete diffusion models for efficient parallel inference, with broader implications for applications such as molecular structure and language generation.
  arXiv  Detail & Related papers  (2026-07-01T10:59:33Z)
• Quantum Multi-Level Estimation of Functionals of Discrete Distributions [23.53427184324404]
  We propose a quantum multi-level estimation framework for a functional $sum_i=1n f(p_i)$ of a discrete distribution.<n>We present efficient quantum estimators for the $q$-Tsallis entropy of discrete distributions.
  arXiv  Detail & Related papers  (2026-05-05T12:25:17Z)
• Uniformity testing when you have the source code [16.232881331802687]
  We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit. We consider the basic task of uniformity testing, which is to decide if the output distribution is uniform on $[d]$ or $epsilon$-far from uniform in total variation distance.
  arXiv  Detail & Related papers  (2024-11-07T18:48:29Z)
• On the average-case complexity of learning output distributions of quantum circuits [33.76498647184212]
  We show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model.<n>This learning model is widely used as an abstract computational model for most generic learning algorithms.
  arXiv  Detail & Related papers  (2023-05-09T20:53:27Z)
• Succinct quantum testers for closeness and $k$-wise uniformity of probability distributions [2.3466828785520373]
  We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. We show that the quantum query complexities for $ell1$- and $ell2$-closeness testing are $O(sqrtn/varepsilon)$ and $O(sqrtnk/varepsilon)$. We propose the first quantum algorithm for this problem with query complexity $O(sqrtnk/varepsilon)
  arXiv  Detail & Related papers  (2023-04-25T15:32:37Z)
• Mind the $\ ilde{\mathcal{O}}$: Asymptotically Better, but Still Impractical, Quantum Distributed Algorithms [0.0]
  We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability. The algorithms achieve a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. An existing framework for using distributed version of Grover's search algorithm to accelerate triangle finding lies at the core of the speedup.
  arXiv  Detail & Related papers  (2023-04-06T02:18:52Z)
• Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyond [89.72693227960274]
  This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. To reduce the number of samples in each round from $m$ to 1, we cast GDRO as a two-player game, where one player conducts and the other executes an online algorithm for non-oblivious multi-armed bandits. In the second scenario, we propose to optimize the average top-$k$ risk instead of the maximum risk, thereby mitigating the impact of distributions.
  arXiv  Detail & Related papers  (2023-02-18T09:24:15Z)
• Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants [8.453228628258778]
  We develop quantum algorithms for sampling logconcave distributions and for estimating their normalizing constants. We exploit quantum analogs of the Monte Carlo method and quantum walks. We also prove a $1/epsilon1-o(1)$ quantum lower bound for estimating normalizing constants.
  arXiv  Detail & Related papers  (2022-10-12T19:10:43Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Quantum Communication Complexity of Distribution Testing [114.31181206328276]
  Two players each receive $t$ samples from one distribution over $[n]$. The goal is to decide whether their two distributions are equal, or are $epsilon$-far apart. We show that the quantum communication complexity of this problem is $tildeO$(tepsilon2))$ qubits when distributions have low $l$-norm.
  arXiv  Detail & Related papers  (2020-06-26T09:05:58Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Locally Private Hypothesis Selection [96.06118559817057]
  We output a distribution from $mathcalQ$ whose total variation distance to $p$ is comparable to the best such distribution. We show that the constraint of local differential privacy incurs an exponential increase in cost. Our algorithms result in exponential improvements on the round complexity of previous methods.
  arXiv  Detail & Related papers  (2020-02-21T18:30:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.