Related papers: Solving quantum dynamics with a Lie algebra decoup…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
Quantum information processing requires overcoming decoherence---the loss of "quantumness" due to the inevitable interaction between the quantum system and its environment. One approach towards a solution is quantum dynamical decoupling---a…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Extracting useful work from quantum systems is a fundamental problem in quantum thermodynamics. In scenarios where rapid protocols are desired -- whether due to practical constraints or deliberate design choices -- a fundamental trade-off…
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. Two examples of normalization in the…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
Refocusing, or dynamical decoupling, is a coherent control technique where the internal dynamics of a quantum system is effectively averaged out by an application of specially designed driving fields. The method has originated in nuclear…
The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction:…
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for…
The preparation of highly entangled many-body systems is one of the central challenges of both basic and applied science. The complexity of interparticle interaction and environment coupling increases rapidly with the number of…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first…
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily…