Related papers: Staggered Quantum Walks with Hamiltonians
Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the…
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…
In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum…
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…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
A general approach to obtain reduced models for a wide class of discrete-time quantum systems is proposed. The obtained models not only reproduce exactly the output of a given quantum model, but are also guaranteed to satisfy physical…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
Advances in recent years have made it possible to explore quantum dots as a viable technology for scalable quantum information processing. Charge qubits for example can be realized in the lowest bound states of coupled quantum dots and the…
The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent…
Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a…
Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…