Related papers: On Complexity and Duality
We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case…
Random permutation circuits were recently introduced as minimal models for local many-body dynamics that can be interpreted both as classical and quantum. Standard dynamical complexity indicators such as damage spreading and…
The property of quantum correlation has been studied in recent years, especially for the quantum and classical correlations affected by environment. The dynamics of quantum and classical correlations in two-qubit system under identical…
We study the equivalence/duality between various non-commutative gauge models at the classical and quantum level. The duality is realised by a linear Seiberg-Witten-like map. The infinitesimal form of this map is analysed in more details.
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Following arXiv:2210.12963 [hep-th], we investigate aspects of the time evolution operator regarded as a density operator and associated entanglement-like structures in various quantum systems. These involve timelike separations and…
We consider different properties of small open quantum systems coupled to an environment and described by a non-Hermitian Hamilton operator. Of special interest is the non-analytical behavior of the eigenvalues in the vicinity of singular…
In relational quantum dynamics, evolution emerges via the correlations between some system of interest and a clock system, which plays the role of a temporal reference frame. Their combined state satisfies a Wheeler-de Witt-like constraint…
We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The…
We introduce the concept of fidelity for dynamical maps in an open quantum system scenario. We derive an inequality linking this quantity to the distinguishability of the inducing environmental states. Our inequality imposes constraints on…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
We study decoherence processes of an S = 1/2 localized spin coupled to conduction band electrons in a metal or a semiconductor via an Ising-like interaction. We derive master equations for the density matrix of the localized spin, by…