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International Conference on Intelligent Computing and Next Generation Networks (ICNGN)

A Long-algorithm Based Variational Quantum Scheme for Pattern Matching Problem

Lu Liu, Xingyu Wu, Chuan Wang

Published Nov 17, 2023• 0 citations
Publisher

Abstract

Grover algorithm is a popular model in quantum computation field and has the advantage of outperforming its classical counterpart in terms of searching speed, hence it has been applied in various domains such as pattern matching. Unfortunately, there are two central issue for this quantum search algorithm, i.e., Grover algorithm, in practical application that firstly it can only achieve a probability nearing 100% rather than exactly, secondly it tends to require a deep quantum circuit. In this work, we propose a Long-algorithm based quantum scheme for pattern matching problem, which can effectively enhance the success probability of quantum pattern matching and mitigate the needs for quantum computing resources. The performance of this scheme is demonstrated numerically, validating our design.

DOI
10.1109/icngn59831.2023.10396781

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Grover algorithm is a popular model in quantum computation field and has the advantage of outperforming its classical counterpart in terms of searching speed, hence it has been applied in various domains such as pattern matching. Unfortunately, there are two central issue for this quantum search algorithm, i.e., Grover algorithm, in practical application that firstly it can only achieve a probability nearing 100% rather than exactly, secondly it tends to require a deep quantum circuit. In this work, we propose a Long-algorithm based quantum scheme for pattern matching problem, which can effectively enhance the success probability of quantum pattern matching and mitigate the needs for quantum computing resources. The performance of this scheme is demonstrated numerically, validating our design.
Abstract Grover quantum algorithm is an unstructured search algorithm that can run on a quantum computer with the complexity of O N\sqrt{N}N​ N , and is one of the typical algorithms of quantum computing. Recently, it has served as a routine for pattern-matching tasks. However, the original Grover search algorithm is probabilistic, which is not negligible for problems involving determinism. Besides that, efficient data loading is also a key challenge for the practical applications of the Grover algorithm. Here in this work, we propose a modified pattern-matching scheme with Long’s quantum search algorithm, in which the quantum circuit structure search algorithm requires fewer multi-qubit quantum gates, and can obtain the desired results deterministically. Then, the comparison of the performance of our scheme and the previous algorithms is presented through numerical simulations, indicating our algorithm is feasible with current quantum technologies which is friendly to noisy intermediate-scale quantum (NISQ) devices.
This article influences the quantum based solutions for traditional pattern matching problem, as the quantum machines can accelerate the computation speed by inherently supporting the parallel executions. The problem identifies solution by suggesting effective algorithms, and as per the classical machines several algorithms are qualified and become criterion for other, importantly noted as Knuth Morris Pratt and Boyer Moore which solves such problem in O(M + N) time. A quantum identical pattern matching algorithms are based upon the principle of high speed Grover's quantum search method which searches an element over unstructured database of "N" elements in O(√N) time. The standard quantum algorithm was proposed by Ramesh and Vinay that could obtain computational speed and provides solution in O(√M + √N) time. We review two already existing quantum based exact and approximate pattern matching algorithms and then by combining the logic of both, a new exact pattern matching algorithm is being proposed which overcomes the algorithmic constraints and substantially proves to be equivalently better than the existing classical and quantum benchmark algorithms. So, this article includes existing and proposed quantum pattern matching algorithms, their flowcharts and examples, mathematical justification over complexity analysis. At last we discuss suitable application domains and further possible variations over the proposed work.
Quantum computing introduces an efficient way for unfolding complex problems on computing systems. It uses concept of superposition and entanglement, & hence supports intrinsic parallelism for obtaining the speedup in context of time over classical computing. Quantum algorithms can be efficiently implemented over quantum computing system. Most popular quantum algorithms like Grover's and Shor's provide a great foundation to specifically design the algorithms. These algorithms work on improving the lower runtime bounds of classical algorithms. Grover's algorithm exhibits a quadratic polynomial speedup while searching an element among `N' elements unstructured database. The algorithmic strategy can be applied over various computer science related applications and some important are being considered in this article i.e. pattern matching, data mining and machine learning. This article explores quantum fundamentals; history based evolution followed by Grover's search algorithm in detail with cascading advantages, limitations & applications and also finally concludes with the significance of quantum computing & quantum algorithmic domains.
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a significant practical advantage when compared to Grover's search algorithm as well as to other quantum pattern matching methods, which rely on building specific queries for particular patterns. Our method makes arbitrary searches on long static databases much more realistic and implementable. Our algorithm, inspired by Grover's, returns the position of the closest substring to a given pattern of size MMM with non-negligible probability in O(N)O(\sqrt{N})O(N​) queries, where NNN is the size of the string. Furthermore, we give the full recipe to implement our algorithm (together with its total circuit complexity), thus offering an oracle-based quantum algorithm ready to be implemented.
The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various types of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there has been no proposal to realize the original motivating application of the algorithm, i.e., the database search or more broadly the pattern matching in a practical setting, mainly due to the technical difficulty in efficiently implementing the data loading and amplitude amplification processes. In this paper, we propose a quantum algorithm that approximately executes the entire Grover database search or pattern matching algorithm. The key idea is to use the recently proposed approximate amplitude encoding method on a shallow quantum circuit, together with the easily implementable inversion-test operation for realizing the projected quantum state having similarity to the query data, followed by the amplitude amplification operation that is independent to the target data index. We provide a thorough demonstration of the algorithm in the problem of image pattern matching.
Grover's algorithm achieves a quadratic speedup for unstructured search when a global oracle for the target set is available. However, its success probability is generally below 100%100\%100%. To overcome this issue, Long presented a modified version of Grover's search algorithm by introducing a phase-matching condition, which can search for the target set with zero theoretical failure rate. Nevertheless, in many applications, the target set is determined by the intersection of multiple constrained sets. Most existing Grover-based methods are limited to the intersection of only two sets and are not always successful in searching for the target set. In this work, based on Long's method, we propose an algorithm for exactly searching the intersection of multiple sets. We derive and prove a phase-matching condition for searching the intersection exactly. Furthermore, we present a quantum circuit that implements exact intersection search. Finally, we support our theoretical results with numerical simulations.