相关论文: Three routes to the exact asymptotics for the one-…

Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The…

The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…

We study the discrete quantum groups $\Gamma$ whose group algebra has an inner faithful representation of type $\pi:C^*(\Gamma)\to M_K(\mathbb C)$. Such a representation can be thought of as coming from an embedding $\Gamma\subset U_K$. Our…

Let $G$ be a strongly regular graph of prime order $p$ with connection degree $k \geq 6$. We prove that the \emph{quantum walk characteristic polynomial} $\chi_q(G,\lambda) \coloneqq \det(\lambda I - U_G)$, where $U_G$ is the coined quantum…

The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point…

Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…

The direct measurement of topological invariants in both engineered and naturally occurring quantum materials is a key step in classifying quantum phases of matter. Here we motivate a toolbox based on time-dependent quantum walks as a…

We report on the theoretical analysis of bosonic and fermionic non-interacting systems in a discrete two-particle quantum walk affected by different kinds of disorder. We considered up to 100-step QWs with a spatial, temporal and…

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables.…

A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…

It is straightforward to give a sum-over-paths expression for the transition amplitudes of a quantum circuit as long as the gates in the circuit are balanced, where to be balanced is to have all nonzero transition amplitudes of equal…

A path integral method, combined with atomistic spin dynamics simulations, has been developed to calculate thermal quantum expectation values using a classical approach. In this study, we show how to treat Hamiltonians with non-linear…

We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…

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…

We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper we define the 3D walk as a product of three coined one-dimensional walks. The…

Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…

A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…