Related papers: Quantum Lattice Boltzmann is a quantum walk
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…
We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein…
We consider quantum walks with position dependent coin on 1D lattice $\mathbb{Z}$. The dispersive estimate $\|U^tP_c u_0\|_{l^\infty}\lesssim (1+|t|)^{-1/3} \|u_0\|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and…
The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs,…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
In this paper we consider quantum walks whose evolution converges to the Dirac equation one in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two and three space dimensions. The…
Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. In this paper, we study the translation of LGCA on quantum computers (QC) using computational basis…
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Presented are several example quantum computing representations of quantum systems with a relativistic energy relation. Basic unitary representations of free Dirac particles and BCS superconductivity are given. Then, these are combined into…
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…
A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design…
Photonic implementations of unitary processes on lattice structures, such as quantum walks, have been demonstrated across various architectures. However, few platforms offer the combined advantages of scalability, reconfigurability, and the…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…