Related papers: Krylov Complexity in Quantum Field Theory
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
We investigate the effect on cosmological evolution of a strongly coupled quantum field that undergoes renormalization group flow from a UV CFT to an IR CFT. The field theory is defined by perturbation of a holographic CFT by a relevant…
Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The…
We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields…
Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has…
We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…
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…
The holographic complexity has been studied in a background which includes a critical point in the dual field theory. We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves…
I suggest the possibility that holographic quantum gravity is, in some sense, equivalent to quantum information theory. Some radical implications would follow. First, the theory of quantum gravity should have no adjustable coupling…
It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The…
The Lanczos algorithm offers a framework for constructing wave functions in closed and open quantum systems from their Hamiltonians. Since the early universe is inherently an open system, we employ this algorithm to investigate Krylov…
We calculate the volume and action forms of holographic complexity for the gravitational collapse of scalar field matter in asymptotically anti-de Sitter spacetime, using numerical methods to reproduce the geometry responding to the…
Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$ spanned by the…
We propose a holographic dictionary which comes from reducing the bulk theories in an asymptotically flat spacetime to its null infinity. A general boundary theory is characterized by a fundamental field, an infinite tower of descendant…
Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…
Carrollian Holography aims to provide a holographic description of quantum gravity in asymptotically flat spacetimes, in terms of a novel kind of `carrollian' conformal field theory defined on the spacetime null conformal boundary…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
We utilize the recent connection between the high energy limit of the double-scaled SYK model and two-dimensional de Sitter solutions of sine dilaton gravity to identify the length of a family of geodesics spanned between future and past…
We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the…