Related papers: From Krylov Complexity to Observability: Capturing…
In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…
In this work, we investigate the Krylov complexity in quantum optical systems subject to time--dependent classical external fields. We focus on various interacting quantum optical models, including a collection of two--level atoms, photonic…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
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…
Quantum reservoir computing is a computing approach which aims at utilising the complexity and high-dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The…
We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to…
We investigate Krylov complexity in open quantum systems using Lindblad master equations for bosonic bath models, with particular emphasis on the Caldeira--Leggett model. Krylov complexity is computed from the moments of the two-point…
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,…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
We propose a way to understand the evolution of an open quantum system using a description that dispenses a continuous evolution in time, by discrete operators entangled states, in its most direct and fundamental way. We show that the…
Quantum reservoir computing is an emerging field in machine learning with quantum systems. While classical reservoir computing has proven to be a capable concept of enabling machine learning on real, complex dynamical systems with many…
We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…
We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry. Our approach combines the operator-algebra quantum error-correction (OAQEC) structure of…
We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for…
Krylov complexity has recently emerged as a useful probe of operator growth and quantum dynamics in many-body systems and holographic dualities. In this paper we study its behavior in the Veneziano--Wosiek model, a supersymmetric matrix…
In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…
In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful…
Quantum Reservoir Computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum…
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…
We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel…