Related papers: Quantum splines
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…
It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop…
In this paper, we study simple splines on a Riemannian manifold $Q$ from the point of view of the Pontryagin maximum principle (PMP) in optimal control theory. The control problem consists in finding smooth curves matching two given tangent…
The basic idea of spin chain engineering for perfect quantum state transfer (QST) is to find a set of coupling constants in the Hamiltonian, such that a particular state initially encoded on one site will evolve freely to the opposite site…
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary…
This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics,…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a…
Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
The notion of quantum speed limit (QSL) refers to the fundamental fact that two quantum states become completely distinguishable upon dynamical evolution only after a finite amount time, called the QSL time. A different, but related concept…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
Quantum initial state estimation through entanglement and continuous measurement is introduced. This paper provides a unified formulation of classical and quantum smoothing and shows a smoothing uncertainty relation. As an example, a…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied…
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…