Related papers: Krylov complexity has it all
In the Wigner-Weyl phase space formulation of quantum mechanics, we analyse the problem of the spreading of an initial state or an initial operator under time evolution when described in terms of the Krylov basis. After constructing the…
Krylov space methods provide an efficient framework for analyzing the dynamical aspects of quantum systems, with tridiagonal matrices playing a key role. Despite their importance, the behavior of such matrices from chaotic to integrable…
We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|\partial_t S_K|\leq 2b_1 \Delta S_K$, where $b_1$ is the first Lanczos…
We study Krylov complexity $C_K$ and operator entropy $S_K$ in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation $S_K\sim…
The operator wavefunction provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature this wavefunction can acquire a phase that…
We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…
We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point…
Dynamical quantum phase transitions, encompassing phenomena like many-body localization transitions and measurement-induced phase transitions, are often characterized and identified through the analysis of quantum entanglement. Here, we…
In this paper we study Krylov complexity in the presence of single and multiple operators in the DSSYK model, where we can use the analytical techniques coming from chord diagrammatics. One of the results we obtain is that it showcases the…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
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…
In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle…
We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the…
We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric.…
We study quantum dynamics generated by time-dependent Hamiltonians in Krylov space, the minimal subspace in which the evolution takes place. We establish a direct link between dynamics in the time-dependent Krylov subspace and the…
We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This…
In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, von Neumann entropy and capacity of entanglement for…
Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a…
We introduce the Krylov distribution $\mathcal{D}(\xi)$, a static Krylov-space diagnostic that characterizes how inverse-energy response is organized in Hilbert space. The central object is the resolvent-dressed state…