Related papers: Staggered Quantum Walks with Hamiltonians
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 computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
Quantum walks have received a great deal of attention recently because they can be used to develop new quantum algorithms and to simulate interesting quantum systems. In this work, we focus on a model called staggered quantum walk, which…
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
As cloud services continue to expand, the security of private data stored and processed in these environments has become paramount. This work delves into quantum homomorphic encryption (QHE), an emerging technology that facilitates secure…
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…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its…
We analyze the equivalence between discrete-time coined quantum walks and Szegedy's quantum walks. We characterize a class of flip-flop coined models with generalized Grover coin on a graph $\Gamma$ that can be directly converted into…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
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…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…