Quantum algorithms for hypergraph simplex finding

• URL: http://arxiv.org/abs/2409.00239v1
• Date: Fri, 30 Aug 2024 20:12:45 GMT
• Title: Quantum algorithms for hypergraph simplex finding
• Authors: Zhiying Yu, Shalev Ben-David,
• Abstract summary: We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be turned into a faster algorithm for finding simplices in rank-$(r-1)$ hypergraphs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be turned into a faster algorithm for finding simplices in rank-$(r-1)$ hypergraphs. We then show that every nested Johnson graph quantum walk (with any constant number of nested levels) can be converted into an adaptive learning graph. Then, we introduce the concept of $\alpha$-symmetric learning graphs, which is a useful framework for designing and analyzing complex quantum search algorithms. Inspired by the work of Le Gall, Nishimura, and Tani (2016) on $3$-simplex finding, we use our new technique to obtain an algorithm for $4$-simplex finding in rank-$4$ hypergraphs with $O(n^{2.46})$ quantum query cost, improving the trivial $O(n^{2.5})$ algorithm.

Related papers

• Quantum Speedup for Hypergraph Sparsification [3.5293335880819483]
  We propose the first quantum algorithm for hypergraph sparsification, addressing an open problem proposed by Apers and de Wolf (FOCS'20)<n>For a weighted hypergraph with $n$ vertices, $m$ hyperedges, and rank $r$, our algorithm outputs a near-linear size $varepsilon$-spectral sparsifier in time $widetilde O(rsqrtmn/varepsilon)$.<n>This algorithm matches the quantum lower bound for constant $r$ and demonstrates quantum speedup when compared with the state-of-the-
  arXiv  Detail & Related papers  (2025-05-03T09:33:46Z)
• Translation-Invariant Quantum Algorithms for Ordered Search are Optimal [1.4249472316161877]
  Quantum computers can achieve a constant-factor speedup, but the best possible coefficient of $log_2n$ for exact quantum algorithms is only known to lie between $(ln2)/pi approx 0.221$ and $4/log_2605 approx 0.433$. We consider a special class of translation-invariant algorithms with no workspace, introduced by Farhi, Goldstone, Gutmann, and Sipser, that has been used to find the best known upper bounds.
  arXiv  Detail & Related papers  (2025-03-27T02:08:16Z)
• Space-Efficient Quantum Error Reduction without log Factors [50.10645865330582]
  We present a new highly simplified construction of a purifier, that can be understood as a weighted walk on a line similar to a random walk interpretation of majority voting. Our purifier has exponentially better space complexity than the previous one, and quadratically better dependence on the soundness-completeness gap of the algorithm being purified.
  arXiv  Detail & Related papers  (2025-02-13T12:04:39Z)
• A Scalable Algorithm for Individually Fair K-means Clustering [77.93955971520549]
  We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. A clustering is then called individually fair if it has centers within distance $delta(x)$ of $x$ for each $xin P$. We show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.
  arXiv  Detail & Related papers  (2024-02-09T19:01:48Z)
• Algoritmo de Contagem Qu\^antico Aplicado ao Grafo Bipartido Completo [0.0]
  Grover's algorithm is capable of finding $k$ elements in an unordered database with $N$ elements using $O(sqrtN/k)$ steps. This work tackles the problem of using the quantum counting algorithm for estimating the value $k$ of marked elements in other graphs.
  arXiv  Detail & Related papers  (2023-12-05T21:15:09Z)
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck [55.22418739014892]
  We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. We apply our algorithm to the quantum information bottleneck with three quantum systems. Our numerical analysis shows that our algorithm is better than their algorithm.
  arXiv  Detail & Related papers  (2023-11-19T00:06:11Z)
• Universal approach to deterministic spatial search via alternating quantum walks [2.940962519388297]
  We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum walks. Our approach is universal because it does not require an instance-specific analysis for different graphs.
  arXiv  Detail & Related papers  (2023-07-30T05:14:19Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Quantitative approach to Grover's quantum walk on graphs [62.997667081978825]
  We study Grover's search algorithm focusing on continuous-time quantum walk on graphs. Instead of finding specific graph topologies convenient for the related quantum walk, we fix the graph topology and vary the underlying graph endowed Laplacians.
  arXiv  Detail & Related papers  (2022-07-04T19:33:06Z)
• Robust Quantum Walk Search Without Knowing the Number of Marked Vertices [0.2320417845168326]
  Existing quantum walk-based search algorithms suffer from the souffl'e problem. We present a new quantum walk-based search framework that achieves robustness without sacrificing the quantum speedup.
  arXiv  Detail & Related papers  (2021-11-17T10:04:44Z)
• On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids [63.75363908696257]
  The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully.
  arXiv  Detail & Related papers  (2021-06-11T09:43:09Z)
• Quantum algorithms for learning a hidden graph and beyond [0.05076419064097732]
  We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We give quantum algorithms that achieve speedups over the best possible classical algorithms in the OR and parity query models. We additionally give a time-efficient quantum algorithm for this problem, based on the algorithm of Ambainis et al. for a "gapped" version of the group testing problem.
  arXiv  Detail & Related papers  (2020-11-17T13:12:43Z)
• A Query-Efficient Quantum Algorithm for Maximum Matching on General Graphs [0.0]
  We design quantum algorithms for maximum matching. In particular, for a graph with $n$ nodes and $m$ edges, our algorithm makes $O(n7/4) queries in the matrix model.
  arXiv  Detail & Related papers  (2020-10-05T20:34:39Z)
• Online Dense Subgraph Discovery via Blurred-Graph Feedback [87.9850024070244]
  We introduce a novel learning problem for dense subgraph discovery. We first propose a edge-time algorithm that obtains a nearly-optimal solution with high probability. We then design a more scalable algorithm with a theoretical guarantee.
  arXiv  Detail & Related papers  (2020-06-24T11:37:33Z)

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.