Related papers: Time Evolution of Complexity: A Critique of Three …
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior.…
Extended Clifford circuits straddle the boundary between classical and quantum computational power. Whether such circuits are efficiently classically simulable seems to depend delicately on the ingredients of the circuits. While some…
The reduced dynamics of an open quantum system obtained from an underlying microscopic Hamiltonian can in general only approximately be described by a time local master equation. The quality of that approximation depends primarily on the…
Aging is a fundamental aspect of living systems that undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. Living systems, known as complex systems, require complexity…
We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single non-degenerate two level system. We analyze how the binary degree of freedom…
For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity…
This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…
It has long been hypothesized that operating close to the critical state is beneficial for natural, artificial and their evolutionary systems. We put this hypothesis to test in a system of evolving foraging agents controlled by neural…
In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A {\bf 209} (1995) 321) or the SDL measure (Phys. Rev. E {\bf 59} (1999) 2). All these…
The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
Background: The complex scaling method (CSM) has been successfully used to describe many-body resonances as eigenvalues of the complex-scaled Hamiltonian in an appropriate $L^2$ basis representation. Its scope has subsequently been extended…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach,…
The complex software systems developed nowadays require assessing their quality and proneness to errors. Reducing code complexity is a never-ending problem, especially in today's fast pace of software systems development. Therefore, the…
We examine an exactly solvable model of decoherence -- a spin-system interacting with a collection of environment spins. We show that in this simple model (introduced some time ago to illustrate environment--induced superselection) generic…