Related papers: Quantum walks in synthetic gauge fields with 3D in…
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…
We present here an all--optical scheme for the experimental realization of a quantum phase gate. It is based on the polarization degree of freedom of two travelling single photon wave-packets and exploits giant Kerr nonlinearities that can…
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as "minimal coupling", and consists of replacing the momentum operators in the Hamiltonian by modified…
Gauge field is essential for exploring novel phenomena in modern physics. However, it has not been realized in the recent breakthrough experiment about two-leg superconducting circuits with transmon qubits [Phys. Rev. Lett. 123, 050502…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a system. These anomalies are at the heart of topological effects in fundamental, electronic, photonic and ultracold atomic systems, where they result…
We study fermionic and bosonic systems coupled to a real or synthetic static gauge field that is quantized, so the field itself is a quantum degree of freedom and can exist in coherent superposition. A natural example is electrons on a…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional,…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
Artificial gauge fields allow uncharged particles to mimic the behavior of charged particles subjected to magnetic fields, providing a powerful platform for exploring topological physics. Neutral particles, like photons, are typically…
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…
Topological gapless phases of matter have been a recent interest among theoretical and experimental condensed matter physicists. Fermionic chains with extended nearest neighbor couplings have been observed to show unique topological…
Dynamic localization, which originates from the phenomena of particle evolution suppression under an externally applied AC electric field, has been simulated by suppressed light evolution in periodically-curved photonic arrays. However,…