Related papers: Quantum walks on embedded hypercubes: Nonsymmetric…
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 staggered quantum walk was recently introduced as a generalization that allows to unify other versions, such as the coined and Szegedy's walk. However, it also produces new forms of quantum walks not covered by previous…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walk and adiabatic quantum computation. In particular, the method can be used to perform an…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…
We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by a weighted loops. First, we analyze search for a single marked vertex, which can be used for state transfer…
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this definition we derive an explicit formula for…
We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…
We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…