Quantum Advantage in Tolerant Junta Testing

• URL: http://arxiv.org/abs/2606.23194v1
• Date: Mon, 22 Jun 2026 11:42:39 GMT
• Title: Quantum Advantage in Tolerant Junta Testing
• Abstract summary: We establish the first super-polynomial quantum advantage for the tolerant $k$-junta testing problem in the adaptive setting.<n>We show that within a certain parameter regime, tolerant $k$-junta testing with high precision can be solved using $mathrmpoly(k)$ quantum queries.
• Score: 0.5442955439283729
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish the first super-polynomial quantum advantage for the tolerant junta testing problem in the adaptive setting. Specifically, we show that within a certain parameter regime, tolerant $k$-junta testing with high precision can be solved using $\mathrm{poly}(k)$ quantum queries, whereas any classical algorithm requires at least $k^{Ω(\log k)}$ queries. The problem of tolerant $k$-junta testing is as follows: given parameters $(k, ε_1, ε_2)$, with $0\le ε_1<ε_2 \le 1/2$, and black-box access to a Boolean function $f$ (defined on $n$ variables), distinguish whether $f$ is $ε_1$-close to some $k$-junta or $ε_2$-far from every $k$-junta. We show the quantum advantage for a range of parameters close to $1/2$, for example, $ε_1 = 1/2-1/k$ and $ε_2 = 1/2-1/(2k^2)$. The (non-adaptive) quantum tester we use was given by a recent work of Bao, Liu, Yao, Ye, and Zhang (SOSA 2026). We slightly adapt their analysis to show that it holds in the above parameter regime. On the other hand, our classical lower bound requires substantial new ideas. Inspired by the lower bound techniques of Chen and Patel (FOCS 2023), we introduce a new hard distribution of ``yes'' instances (i.e., instances with distance at most $ε_1$ to $k$-juntas) that is based on planting an ``approximate-junta'' as follows: we randomly pick $k$ out of $n$ coordinates, and for each fixing of the $k$ coordinates, the $2^{n-k}$ values in the restricted subcube are drawn randomly except for the set of points in an error-correcting code on which we place the same random bit. We show that this distribution is much closer to $k$-juntas than the uniform distribution, but on the other hand, they are indistinguishable with respect to any classical algorithm making $k^{o(\log k)}$ queries.

Related papers

• Quantum Approximate Counting with Bernoulli Oracles [3.8743350688734988]
  We prove an upper bound of $tildeO!big(fracsqrt+frac1sqrtbig)$ queries, achieving a quadratic speedup over classical sampling.<n>We complement this upper bound with a near-matching lower bound of $(sqrt/())$ via a new composition theorem for the quantum adversary method.
  arXiv  Detail & Related papers  (2026-09-07T15:13:44Z)
• Sublinear Time Quantum Sensitivity Sampling [57.356528942341534]
  We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems.<n>Our framework provides a streamlined approach for constructing coresets and offers significant runtime improvements in applications such as clustering, regression, and low-rank approximation.
  arXiv  Detail & Related papers  (2025-09-20T20:18:49Z)
• Efficient Non-Adaptive Quantum Algorithms for Tolerant Junta Testing [18.89209417623036]
  We consider the problem of deciding whether an $n$-qubit unitary is $varepsilon$-close to some $k$-junta or $varepsilon$-far from every $k$-junta.<n>We adapt the first two quantum algorithms to be implemented using only single-qubit operations, thereby enhancing experimental feasibility.
  arXiv  Detail & Related papers  (2025-08-24T11:15:40Z)
• Tolerant Quantum Junta Testing [0.0]
  Tolerant junta testing is more general and challenging than the standard version. We present the first algorithm to decide whether a unitary is $epsilon$-junta or is $epsilon$-far from any quantum $k$-junta.
  arXiv  Detail & Related papers  (2024-11-04T16:34:50Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• 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)
• Online Learning with Adversaries: A Differential-Inclusion Analysis [52.43460995467893]
  We introduce an observation-matrix-based framework for fully asynchronous online Federated Learning with adversaries. Our main result is that the proposed algorithm almost surely converges to the desired mean $mu.$ We derive this convergence using a novel differential-inclusion-based two-timescale analysis.
  arXiv  Detail & Related papers  (2023-04-04T04:32:29Z)
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
  We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
  arXiv  Detail & Related papers  (2022-12-03T02:45:23Z)
• The Sparse Hausdorff Moment Problem, with Application to Topic Models [5.151973524974052]
  We give an algorithm for identifying a $k$-mixture using samples of $m=2k$ iid binary random variables. It suffices to know the moments to additive accuracy $w_mincdotzetaO(k)$.
  arXiv  Detail & Related papers  (2020-07-16T04:23:57Z)
• 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)
• Quantum Coupon Collector [62.58209964224025]
  We study how efficiently a $k$-element set $Ssubseteq[n]$ can be learned from a uniform superposition $|Srangle of its elements. We give tight bounds on the number of quantum samples needed for every $k$ and $n$, and we give efficient quantum learning algorithms.
  arXiv  Detail & Related papers  (2020-02-18T16:14:55Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)

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.