Related papers: On Krylov Complexity
In holography, the complexity--momentum correspondence relates the increasing momentum of a point particle falling into an eternal black hole to the rate of growth of the Krylov complexity of the dual boundary state, a conjecture…
The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual…
We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, i.e. anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates…
In this work, we investigate the quantum chaos in various $T\bar{T}$-deformed SYK models with finite $N$, including the SYK$_4$, the supersymmetric SYK$_4$, and the SYK$_2$ models. We numerically study the evolution of the spectral form…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
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…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
We propose a two-dimensional (2d) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set…
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic…
The Jarzynski identity can describe small-scale nonequilibrium systems through stochastic thermodynamics. The identity considers fluctuating trajectories in a phase space. The complexity geometry frames the discussions on quantum…
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…
In this paper, we studied a set of generalised Krylov complexity for operator growth. We demonstrate their universal features at both initial times and long times using half-analytical technique as well as numerical results. In particular,…
In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
In this paper, we examine the proposed first law of holographic complexity through studying different perturbations around various spacetime backgrounds. We present a general expression for the variation of the holographic complexity on…
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…