Related papers: Time Evolution of Complexity: A Critique of Three …
We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…
Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant…
Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative…
We show that the characteristic function of the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function between an initial…
Continuing generation of novelty, complexity, and adaptation are well-established as core aspects of open-ended evolution. However, it has yet to be firmly established to what extent these phenomena are coupled and by what means they…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by…
We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the…
A major aim of evolutionary biology is to explain the respective roles of adaptive versus non-adaptive changes in the evolution of complexity. While selection is certainly responsible for the spread and maintenance of complex phenotypes,…
We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other,…
In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we…
Understanding the evolution of complexity is an important topic in a wide variety of academic fields. Implications of better understanding complexity include increased knowledge of major evolutionary transitions and the properties of living…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
Societal complexity may be at a historical peak. Distinct from entropy, complexity tends to rise as systems move away from order, crest at an intermediate state, and decline as entropy continues increasing. The use of a thermodynamic…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…