Related papers: On Quantum Integrable Systems
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labellings of…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
This paper is intended to serve as a review of a series of papers with Nikita Nekrasov, where we achieved several important results concerning the relation between the moduli space of instantons and classical integrable systems. We derive…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
A kinetic theory for quantum Langmuir waves interacting nonlinearly with quantum ion-acoustic waves is derived. The formulation allows for a statistical analysis of the quantum correction to the Zakharov system. The influence of a…
Quantum information can be processed using large ensembles of ultracold and trapped neutral atoms, building naturally on the techniques developed for high-precision spectroscopy and metrology. This article reviews some of the most important…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…
We describe a parametric frequency conversion scheme for trapped charged particles which enables a coherent interface between atomic and solid-state quantum systems. The scheme uses geometric non-linearities of the potential of a coupling…
We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle…