Related papers: Quantum Walks for Chemical Reaction Networks
Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the…
A chemical reaction mechanism (CRM) is a sequence of molecular-level events involving bond-breaking/forming processes, generating transient intermediates along the reaction pathway as reactants transform into products. Understanding such…
Link prediction is one of the fundamental problems in graph theory, critical for understanding and forecasting the evolution of complex systems like social and biological networks. While classical heuristics capture certain aspects of graph…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
We present a quantum algorithm for ranking the nodes on a network in their order of importance. The algorithm is based on a directed discrete-time quantum walk, and works on all directed networks. This algorithm can theoretically be applied…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
Quantum walks (QWs) represent pillars of quantum dynamics and information processing. They provide a powerful framework for simulating quantum transport, designing search algorithms, and enabling universal quantum computation. Several…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We address the problem of routing quantum and classical information from one sender to many possible receivers in a network. By employing the formalism of quantum walks, we describe the dynamics on a discrete structure based on a complete…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…
We prove that a quantum walk can detect the presence of a marked element in a graph in $O(\sqrt{WR})$ steps for any initial probability distribution on vertices. Here, $W$ is the total weight of the graph, and $R$ is the effective…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end we design, model…