Related papers: Quantum algorithm for de novo DNA sequence assembl…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
In this study, we explore how quantum pathfinding algorithm called Gaussian Amplitude Amplification (GAA) can be used to solve the DNA sequencing problem. To do this, sequencing by hybridization was assumed wherein short fragments of the…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
Genome assembly is a prominent problem studied in bioinformatics, which computes the source string using a set of its overlapping substrings. Classically, genome assembly uses assembly graphs built using this set of substrings to compute…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…
In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
We develop a general framework to construct quantum algorithms that detect if a $3$-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept…
The problem of assembling DNA fragments starting from imperfect strings given by a sequencer, classified as NP hard when trying to get perfect answers, has a huge importance in several fields, because of its relation with the possibility of…
Reconstructing DNA sequences without a reference, known as de novo assembly, is a complex computational task involving the alignment of overlapping fragments. To address this problem, a usual strategy is to map the assembly to a Quadratic…
De novo genome assembly is challenging in highly repetitive regions; however, reference-guided assemblers often suffer from bias. We propose a framework for pangenome-guided sequence assembly, which can resolve short-read data in complex…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
Sequence Alignment is the process of aligning biological sequences in order to identify similarities between multiple sequences. In this paper, a Quantum Algorithm for finding the optimal alignment between DNA sequences has been…
Control and characterization of networks is a paramount step for the development of many quantum technologies. Even for moderate-sized networks, this amounts to explore an extremely vast parameters space in search for the couplings defining…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…