From Bit-Parallelism to Quantum String Matching for Labelled Graphs

• URL: http://arxiv.org/abs/2302.02848v2
• Date: Fri, 14 Apr 2023 12:40:39 GMT
• Title: From Bit-Parallelism to Quantum String Matching for Labelled Graphs
• Authors: Massimo Equi, Arianne Meijer - van de Griend, Veli M\"akinen
• Abstract summary: Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. We show that a simple bit-parallel algorithm on such restricted family of graphs can indeed be converted into a realistic quantum algorithm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in $O(n^2/w)$ time. In a reasonable classical model of computation, one can assume $w=\Theta(\log n)$, and obtaining significantly better speed-ups is unlikely in the light of conditional lower bounds obtained for such problems. In this paper, we study the connection of bit-parallelism to quantum computation, aiming to see if a bit-parallel algorithm could be converted to a quantum algorithm with better than logarithmic speed-up. We focus on string matching in labeled graphs, the problem of finding an exact occurrence of a string as the label of a path in a graph. This problem admits a quadratic conditional lower bound under a very restricted class of graphs (Equi et al. ICALP 2019), stating that no algorithm in the classical model of computation can solve the problem in time $O(|P||E|^{1-\epsilon})$ or $O(|P|^{1-\epsilon}|E|)$. We show that a simple bit-parallel algorithm on such restricted family of graphs (level DAGs) can indeed be converted into a realistic quantum algorithm that attains subquadratic time complexity $O(|E|\sqrt{|P|})$.

Related papers

• Quantum State Learning Implies Circuit Lower Bounds [2.2667044928324747]
  We establish connections between state tomography, pseudorandomness, quantum state, circuit lower bounds. We show that even slightly non-trivial quantum state tomography algorithms would lead to new statements about quantum state synthesis.
  arXiv  Detail & Related papers  (2024-05-16T16:46:27Z)
• Quantum algorithms for Hopcroft's problem [45.45456673484445]
  We study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. The classical complexity of this problem is well-studied, with the best known algorithm running in $O(n4/3)$ time. Our results are two different quantum algorithms with time complexity $widetilde O(n5/6)$.
  arXiv  Detail & Related papers  (2024-05-02T10:29:06Z)
• 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)
• Near-Optimal Quantum Algorithms for Bounded Edit Distance and Lempel-Ziv Factorization [2.684542790908823]
  We present a quantum $tildeO(sqrtnk+k2)$-time algorithm that uses $tildeO(sqrtnz)$ queries, where $tildeO(cdot)$ hides polylogarithmic factors. Our second main contribution is a quantum algorithm that achieves the optimal time complexity of $tildeO(sqrtnz)$.
  arXiv  Detail & Related papers  (2023-11-03T09:09:23Z)
• 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)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model [0.0]
  We show how to convert bit-parallelism of quadratic time solvable problems into quantum algorithms that attain speed-ups with factor $n$. We first show that the famous $O(n2/w)$ time bit-parallel algorithm of Myers (J. ACM, 1999) can be adjusted to work without arithmetic + operations.
  arXiv  Detail & Related papers  (2021-12-24T09:26:55Z)
• Time and Query Optimal Quantum Algorithms Based on Decision Trees [2.492300648514128]
  We show that a quantum algorithm can be implemented in time $tilde O(sqrtGT)$. Our algorithm is based on non-binary span programs and their efficient implementation.
  arXiv  Detail & Related papers  (2021-05-18T06:51:11Z)
• Classical algorithms for Forrelation [2.624902795082451]
  We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms of its query complexity. We show that the graph-based forrelation problem can be solved on a classical computer in time $O(n)$ for any bipartite graph.
  arXiv  Detail & Related papers  (2021-02-13T17:25:41Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• Second-order Conditional Gradient Sliding [79.66739383117232]
  We present the emphSecond-Order Conditional Gradient Sliding (SOCGS) algorithm. The SOCGS algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. It is useful when the feasible region can only be accessed efficiently through a linear optimization oracle.
  arXiv  Detail & Related papers  (2020-02-20T17:52:18Z)

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.