相关论文: Krylov Complexity in Canonical Quantum Cosmology

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 extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…

The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian…

We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism,…

In this work were studied quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity's theory proposed by Ho\v{r}ava, the so-called Ho\v{r}ava-Lifshitz theory of the gravity. It was used the Ho\v{r}ava…

We consider the complex SYK model in the double-scaling limit. We obtain the transfer matrix for the grand canonical ensemble and symmetrize it. In the (n,Q)- basis of chord states, the grand canonical transfer matrix is block diagonal,…

Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that…

Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the…

We consider a k=0 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state…

We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…

Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the NISQ era, because of its superb performance and compatibility with current quantum devices. By harnessing the…

Krylov subspace methods quantify operator growth in quantum many-body systems through Lanczos coefficients that encode how operators spread under time evolution. Although these diagnostics were originally motivated by questions of chaos and…

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss…

We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability…

We extend the CV conjecture to quantum states of two-mode Hermitian systems using the framework of information geometry. Specifically, we conjecture that the Krylov complexity of a quantum state equals the volume of the Fubini-Study metric.…

In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement…

We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a…

Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological…

The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…