Related papers: About mathematical apparatus of many body quantum …
The recent advancement of quantum computer hardware offers the potential to simulate quantum many-body systems beyond the capability of its classical counterparts. However, most current works focus on simulating the ground-state properties…
The classical Landau-Lifshitz-Gilbert (LLG) equation has long served as a cornerstone for modeling magnetization dynamics in magnetic systems, yet its classical nature limits its applicability to inherently quantum phenomena such as…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
We describe a numerical method which allows us to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent…
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…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable…
We study the dynamics of a complex open quantum many-body system. The coupling to external degrees of freedom can be viewed as a coupling to a radiation field, to continuum states or to a measuring apparatus. This perturbation is treated in…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a…
We propose a new representation for several quantum master equations in so-called quasithermodynamic form. This representation (when it exists) let one to write down dynamical equations both for diagonal and non-diagonal elements of density…
We discuss three different aspects of the quantum dynamics of bio-molecular systems and more generally complex networks in the presence of strongly coupled environments. Firstly, we make a case for the systematic study of fundamental…
We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. The interest often lies in estimating observables rather than explicitly obtaining…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex…
We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin…