Related papers: On The Evolution Of Operator Complexity Beyond Scr…
We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
We study the temporal evolution of the circuit complexity after the local quench where two harmonic chains are suddenly joined, choosing the initial state as the reference state. We discuss numerical results for the complexity for the…
The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors and decoherence. Here, we provide a universal framework…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is…
In his seminal work with NK algorithms, Kauffman noted that fitness outcomes from algorithms navigating an NK landscape show a sharp decline at high complexity arising from pervasive interdependence among problem dimensions. This phenomenon…
The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…
We study scrambling in connection to multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are…
The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter…
We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is…
We show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced $k$-clique and a graph in which all k-subgraphs have density at most $1-\epsilon$, requires $n^{\tilde \Omega(log n)}$…
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…
Observations are an essential component of the simulation based studies on artificial-evolutionary systems (AES) by which entities are identified and their behavior is observed to uncover higher-level "emergent" phenomena. Because of the…
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous…
The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…