字符串处理的量子算法

Quantum Algorithms for the Most Frequently String Search, Intersection of Two String Sequences and Sorting of Strings Problems

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the string that occurs in the sequence most often. We propose a quantum algorithm that has a query complexity $\tilde{O}(n \sqrt{k})$. This algorithm shows speed-up comparing with the deterministic algorithm that requires $Ω(nk)$ queries. The second one is searching intersection of two sequences of strings. All strings have the same length $k$. The size of the firs…

在线性时间内计数反交换Pauli对

Counting anticommuting Pauli pairs in linear time

本文提出一种线性时间算法，用于在受限局部性范围内高效计算Pauli字符串的反交换对数，通过维护子模式计数和子集ζ恒等式实现。

PauLIB：用于处理泡利字符串的高性能库

PauLIB: A High-Performance Library for Processing Pauli Strings

提出基于位打包二元辛表示、排序数组布局和结构体数组内存布局的C++20库PauLIB，通过SIMD向量化和多线程合并显著加速泡利字符串处理，在500量子比特下单次泡利字符串乘法比PauliEngine快14倍，哈密顿量外积乘法快约10倍，贪心对易分组比PennyLane快21000倍，内存占用降低7.3倍。

Quantum computational tensor network on string-net condensate

The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the most basic example of the string-net condensate, namely the $Z_2$ gauge string-net condensate on the two-dimensional hexagonal lattice, and show that the universal measurement-based quantum computation (in the sense of the quantum computational webs) is possible on it by using the framework of the quantum computational tensor network. This result implies that e…

Near-Optimal Quantum Algorithms for String Problems

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology literature since the 1970s, and are known to be solvable by near-linear time classical algorithms. In this work, we give quantum algorithms for these problems with near-optimal query complexities and time complexities. Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in $\tilde O(n^{2/3})$ time, improving upon the rece…

多字符串匹配问题的量子算法

Quantum Algorithm for the Multiple String Matching Problem

本文针对多字符串匹配问题提出一种量子算法，查询复杂度为 O(n+√(mL log n)+m log n)，时间复杂度为 O^*(n+√(mL))，达到量子下界（仅差对数因子），可视为 Aho-Corasick 算法的量子类比，在长单词字典场景下优势显著。

基于弦图的混合量子-经典机器学习

Hybrid Quantum-Classical Machine Learning with String Diagrams

本文提出用带函子盒的弦图形式化描述混合量子-经典算法，通过松弛幺半函子刻画量子-经典接口与测量限制，为混合量子机器学习建立捕捉量子-经典交互特征的指称语义基础。

Classical and Quantum Algorithms for Constructing Text from Dictionary Problem

We study algorithms for solving the problem of constructing a text (long string) from a dictionary (sequence of small strings). The problem has an application in bioinformatics and has a connection with the Sequence assembly method for reconstructing a long DNA sequence from small fragments. The problem is constructing a string $t$ of length $n$ from strings $s^1,\dots, s^m$ with possible intersections. We provide a classical algorithm with running time $O\left(n+L +m(\log n)^2\right)=\tilde{O}(n+L)$ where $L$ is the sum of lengths of $s^1,\dots,s^m$. We provide a quantum algorithm with runnin…

用于字典序最小字符串旋转的量子算法

Quantum Algorithm for Lexicographically Minimal String Rotation

本文提出求解字典序最小字符串旋转的O(n^{3/4})量子查询算法，平均复杂度达渐近最优，且优于经典随机算法，可应用于苯环识别等场景。

量子遇上细粒度复杂性：字符串问题的次线性时间量子算法

Quantum Meets Fine-grained Complexity: Sublinear Time Quantum Algorithms for String Problems

本文针对最长公共子串、最长回文子串和Ulam距离三个字符串问题，提出了次线性时间量子算法并给出量子下界，揭示了LCS与LPS量子复杂性的差异。

String Comparison on a Quantum Computer Using Hamming Distance

The Hamming distance is ubiquitous in computing. Its computation gets expensive when one needs to compare a string against many strings. Quantum computers (QCs) may speed up the comparison. In this paper, we extend an existing algorithm for computing the Hamming distance. The extension can compare strings with symbols drawn from an arbitrary-long alphabet (which the original algorithm could not). We implement our extended algorithm using the QisKit framework to be executed by a programmer without the knowledge of a QC (the code is publicly available). We then provide four pedagogical examples:…

ACSS-q: Algorithmic complexity for short strings via quantum accelerated approach

In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is restricted in time and space resources to make it computable in approximating the target metrics. The quantum circuit design based on our earlier work that allows executing a superposition of automata is presented. As a use-case, an application framework for protein-protein interaction ontology based on algorithmic complexity is proposed. Using small-scale …