Related papers: Using Hilbert transform and classical chains to si…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…
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 standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
We simulate dynamics of many-particle systems of bosons and fermions using discrete time quantum walks on lattices. We present a computational proof of a behavior of the simulated systems similar to the one observed in Hamiltonian dynamics…
The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to…
Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by…
We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…