Related papers: Semiclassical evaluation of quantum fidelity
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum…
The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electron charges as a trace/diagonal of a matrix function,…
The Loschmidt echo (LE) is a measure of the sensitivity of quantum mechanics to perturbations in the evolution operator. It is defined as the overlap of two wave functions evolved from the same initial state but with slightly different…
We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…
This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the…
We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation $V(q,t)$ with typical strength $\hbar/\tau_{V}$. The perturbation represents the action of an uncontrolled environment…
We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…
We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random…
We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival…
We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that…
While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects.…
Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of…
We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial…
We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson…
We introduce a simulation-free method to estimate the fidelity of large quantum circuits based on the order statistics of measured output probabilities from highly entangled, chaotic states. The approach requires only the…
In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A…