Related papers: Krylov Complexity in Calabi-Yau Quantum Mechanics
We show that Hall's exact uncertainty relation acquires a simple geometric form in the Krylov basis generated by the Liouvillian. In this canonical operator frame, the uncertainty equality implies that the operator amplitude vector evolves…
The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…
We study the equilibration times $T_\text{eq}$ of local observables in quantum chaotic systems by considering their auto-correlation functions. Based on the recursion method, we suggest a scheme to estimate $T_\text{eq}$ from the…
We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators…
We explore Krylov complexity in the BMN matrix model following a systematic reduction of it, known as the pulsating fuzzy sphere model. We present an analytical setup that allows us to calculate Lanczos coefficients in both large and small…
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…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
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…
In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL$(2,\mathbb{R})$ Hamiltonians. In the vacuum state, we find that the K-complexity exhibits a universal phase structure. The…
We study growth quenches, which are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models, such as the East-West model. We point out a formal analogy with the dynamics of a local…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
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…
We consider the approximation of $B^T (A+sI)^{-1} B$ for large s.p.d. $A\in\mathbb{R}^{n\times n}$ with dense spectrum and $B\in\mathbb{R}^{n\times p}$, $p\ll n$. We target the computations of Multiple-Input Multiple-Output (MIMO) transfer…
Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and…
Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at…
We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…