Related papers: Krylov's State Complexity and Information Geometry…
The exchange of information between an open quantum system and its environment, especially the backflow of information from the environment to the open system associated with quantum notions of non-Markovianity, is a widely discussed topic…
Geometric properties of evolutionary graph states of spin systems generated by the operator of evolution with Ising Hamiltonian are examined, using their relationship with fluctuations of energy. We find that the geometric characteristics…
We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a…
We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an…
Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of…
We continue the analysis of the Krylov complexity in the IP matrix model. In a previous paper, for a fundamental operator, it was shown that at zero temperature, the Krylov complexity oscillates and does not grow, but in the infinite…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric…
We investigate holographic Krylov complexity in fully top-down AdS$_3$ and AdS$_2$ supergravity backgrounds dual to two-dimensional linear-quiver SCFTs and one-dimensional conformal quantum mechanics. In these geometries, the warp factors,…
Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies…
With the growth of geometric science, including the methods of exploring the world of information by means of modern geometry, there has always been a mysterious and fascinating ambiguous link between geometric, topological and dynamical…
The evolutions of states is described corresponding to the Glauber dynamics of an infinite system of interacting particles in continuum. The description is conducted on both micro- and mesoscopic levels. The microscopic description is based…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
In this paper, we construct 2-dimensional bipartite cluster states and perform single-qubit measurements on the bulk qubits. We explore the entanglement scaling of the unmeasured 1-dimensional boundary state and show that under certain…
We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the…
For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the…
In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
We establish a systematic framework for studying quantum computational complexity of Gaussian states of charged systems based on Nielsen's geometric approach. We use this framework to examine the effect of a chemical potential on the…