Related papers: Dynamics of continuous-time quantum walks in restr…
Quantum walks often provide telling insights about the structure of the system on which they are performed. In PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…
We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…
We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise:…
Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples…
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…
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…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
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…
We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315)…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
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…
The analysis of logarithmic return distributions defined over large time scales is crucial for understanding the long-term dynamics of asset price movements. For large time scales of the order of two trading years, the anticipated Gaussian…
Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy…