Related papers: Decoherence enhances performance of quantum walks …
De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
In this dissertation we demonstrate that the continuous-time quantum walk models remain powerful for nontrivial graph structures. We consider two aspects of this problem. First, it is known that the standard Continuous-Time Quantum Walk…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position…
Quantum walk acts obviously different from its classical counterpart, but decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of quantum walk under different…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum…
We investigate the stability of continuous-time quantum walks (CTQW) across cycle, complete, star, Erd\H{o}s-R\'enyi, small-world, and scale-free topologies under energy-based intrinsic decoherence, node-based Haken-Strobl noise, and…
We present a 2-local quantum algorithm for graph isomorphism GI based on an adiabatic protocol. By exploiting continuous-time quantum-walks, we are able to avoid a mere diffusion over all possible configurations and to significantly reduce…