{"title":"一种量子字符串匹配算法","authors":"Konstantinos Prousalis, Asimakis Kydros, Nikos Konofaos","doi":"10.1002/qute.202400250","DOIUrl":null,"url":null,"abstract":"<p>A novel quantum algorithm for string-matching is introduced that significantly enhances the complexity of this fundamental operation, essential in numerous computing applications. The algorithm is designed as a composite quantum denoising procedure applied to a quantum-generated dot-matrix plot, which is treated as an image. This approach effectively identifies regions of similarity between two input strings of lengths <i>N</i> and <i>M</i>. For strings of equal length, the algorithm achieves a time complexity of <span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <mrow>\n <mi>N</mi>\n <mo>+</mo>\n <mi>l</mi>\n <mi>o</mi>\n <mi>g</mi>\n <mrow>\n <mo>(</mo>\n <mi>N</mi>\n <mo>)</mo>\n </mrow>\n <mo>+</mo>\n <mn>6</mn>\n <msup>\n <mi>N</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n <mo>)</mo>\n </mrow>\n <annotation>$O( {N + log( N ) + 6{{N}^2}} )$</annotation>\n </semantics></math> and a space complexity of <span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <mrow>\n <mi>l</mi>\n <mi>o</mi>\n <mi>g</mi>\n <mo>(</mo>\n <mrow>\n <mn>2</mn>\n <mi>N</mi>\n </mrow>\n <mo>)</mo>\n </mrow>\n <mo>)</mo>\n </mrow>\n <annotation>$O( {log( {2N} )} )$</annotation>\n </semantics></math>, demonstrating a clear advantage in quantum computational efficiency.</p>","PeriodicalId":72073,"journal":{"name":"Advanced quantum technologies","volume":"8 3","pages":""},"PeriodicalIF":4.4000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qute.202400250","citationCount":"0","resultStr":"{\"title\":\"A Quantum String-Matching Algorithm\",\"authors\":\"Konstantinos Prousalis, Asimakis Kydros, Nikos Konofaos\",\"doi\":\"10.1002/qute.202400250\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A novel quantum algorithm for string-matching is introduced that significantly enhances the complexity of this fundamental operation, essential in numerous computing applications. The algorithm is designed as a composite quantum denoising procedure applied to a quantum-generated dot-matrix plot, which is treated as an image. This approach effectively identifies regions of similarity between two input strings of lengths <i>N</i> and <i>M</i>. For strings of equal length, the algorithm achieves a time complexity of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>O</mi>\\n <mo>(</mo>\\n <mrow>\\n <mi>N</mi>\\n <mo>+</mo>\\n <mi>l</mi>\\n <mi>o</mi>\\n <mi>g</mi>\\n <mrow>\\n <mo>(</mo>\\n <mi>N</mi>\\n <mo>)</mo>\\n </mrow>\\n <mo>+</mo>\\n <mn>6</mn>\\n <msup>\\n <mi>N</mi>\\n <mn>2</mn>\\n </msup>\\n </mrow>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$O( {N + log( N ) + 6{{N}^2}} )$</annotation>\\n </semantics></math> and a space complexity of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>O</mi>\\n <mo>(</mo>\\n <mrow>\\n <mi>l</mi>\\n <mi>o</mi>\\n <mi>g</mi>\\n <mo>(</mo>\\n <mrow>\\n <mn>2</mn>\\n <mi>N</mi>\\n </mrow>\\n <mo>)</mo>\\n </mrow>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$O( {log( {2N} )} )$</annotation>\\n </semantics></math>, demonstrating a clear advantage in quantum computational efficiency.</p>\",\"PeriodicalId\":72073,\"journal\":{\"name\":\"Advanced quantum technologies\",\"volume\":\"8 3\",\"pages\":\"\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qute.202400250\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced quantum technologies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/qute.202400250\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced quantum technologies","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qute.202400250","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
摘要
介绍了一种新的量子字符串匹配算法，它大大提高了这一基本操作的复杂性，这在许多计算应用中是必不可少的。该算法被设计为一种复合量子去噪过程，应用于量子生成的点阵图，并将其作为图像处理。该方法有效地识别长度为N和m的两个输入字符串之间的相似区域。对于长度相等的字符串，该算法的时间复杂度为O (N + l) O (N) + 6N 2)$ O({N + log(N) + 6{{N}^2}})$，空间复杂度为O(l O g（2n）))$ O({log({2N})})$，显示了量子计算效率的明显优势。
A novel quantum algorithm for string-matching is introduced that significantly enhances the complexity of this fundamental operation, essential in numerous computing applications. The algorithm is designed as a composite quantum denoising procedure applied to a quantum-generated dot-matrix plot, which is treated as an image. This approach effectively identifies regions of similarity between two input strings of lengths N and M. For strings of equal length, the algorithm achieves a time complexity of and a space complexity of , demonstrating a clear advantage in quantum computational efficiency.
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