Related papers: Parameterized quantum algorithms for closest strin…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
A $\mu$-biased Max-CSP instance with predicate $\psi:\{0,1\}^r \to \{0,1\}$ is an instance of Constraint Satisfaction Problem (CSP) where the objective is to find a labeling of relative weight at most $\mu$ which satisfies the maximum…
The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas -- including not only…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
Recently, many new challenges in Compressed Sensing (CS), such as block sparsity, arose. In this paper, we present a new algorithm for solving CS with block sparse constraints (BSC) in complex fields. Firstly, based on block sparsity…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to…
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…
In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
String matching is a fundamental problem in computer science, with critical applications in text retrieval, bioinformatics, and data analysis. Among the numerous solutions that have emerged for this problem in recent decades,…
Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…