Related papers: Quantum Dynamics in Krylov Space: Methods and Appl…
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace $H_{0}$ of dimensionality $M_{0}$, which evolves to populate system subspaces…
We establish a unified framework connecting decoherence and quantum complexity. By vectorizing the density matrix into a pure state in a double Hilbert space, a decoherence process is mapped to an imaginary-time evolution. Expanding this…
In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
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…
The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
We explore Krylov complexity for two exactly solvable models, one in the Wheeler-DeWitt (WDW) quantum cosmology and another in loop quantum cosmology (LQC), for a spatially flat, homogeneous, and isotropic universe sourced with a massless…
When the dynamics of a quantum system of interest is known, an informationally-complete set of observables is not needed for state reconstruction via tomographic techniques: letting the system evolve before performing the measurement allows…
In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature…
We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…
We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…