相关论文: Two-Particle Scattering on Non-Translation Invaria…

We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…

We study the transport of few-photon states in an open disordered nonlinear photonic lattice. More specifically, we consider a waveguide quantum electrodynamics (QED) setup where photons are scattered from a chain of nonlinear resonators…

We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its…

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based…

We demonstrate tunneling spectroscopy of synthetic quantum matter in superconducting circuit lattices. We measure site-resolved excitation spectra by coupling the lattice to engineered driven-dissipative particle baths that serve as local…

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, 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…

We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…

Based on the analytic model of Feshbach resonances in harmonic traps described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced that provides an accurate description of two atoms in an optical lattice at a Feshbach…

One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…

In the case of compact quantum graphs, many-particle models with singular two-particle interactions where introduced in [arXiv:1207.5648, arXiv:1112.4751] to provide a paradigm for further studies on many-particle quantum chaos. In this…

The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…

Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged…

We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…

Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…

Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…

Based on the Dirac representation of Maxwell equations we present an explicit, discrete space-time, quantum walk-inspired algorithm suitable for simulating the electromagnetic wave propagation and scattering from inhomogeneities within…

Dynamical properties of two bosonic quantum walkers in a one-dimensional lattice are studied theoretically. Depending on the initial state, interactions, lattice tilting, and lattice disorder, whole plethora of different behaviors are…

A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The…