Related papers: On The Evolution Of Operator Complexity Beyond Scr…
In closed generic many-body systems, unitary evolution disperses local quantum information into highly non-local objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the…
The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in…
This is a review of group entropy and its application to permutation complexity. Specifically we revisit a new approach to the notion of complexity in time serie analysis, based on both permutation entropy and group entropy. As a result,…
We introduce Krylov spread complexity in the context of black hole scattering by studying highly excited string states (HESS). Krylov complexity characterizes chaos by quantifying the spread of a state or operator under a known Hamiltonian.…
Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relation to quantum chaotic evolution…
The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the…
Black-box complexity theory provides lower bounds for the runtime of black-box optimizers like evolutionary algorithms and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
A fundamental problem in quantum thermodynamics is to properly quantify the work extractable from out-of-equilibrium systems. While for closed systems, maximum quantum work extraction is defined in terms of the ergotropy functional, this…
We study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK) based quench protocol, we show that the time evolution of simple…
We develop a theory of classical complexity. We study the relations between classical complexity and entropy, and conjecture that in an isolated system, classical absolute complexity always tends to grow, until it reaches its maximum. We…
The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\hbar$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of…
For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper we analyse the…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
We present a comprehensive investigation of $\epsilon$-entropy, $h(\epsilon)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the…
We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…