Related papers: Quantum simulations of classical random walks and …
Fault-tolerant quantum computation using lattice surgery can be abstracted as operations on graphs, wherein each logical qubit corresponds to a vertex of the graph, and multi-qubit measurements are accomplished by connecting the vertices…
A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
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…
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain; perfect state transfer,…
We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
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 a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…
We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the…
Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
Closed timelike curves are among the most controversial features of modern physics. As legitimate solutions to Einstein's field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…