相关论文: Accuracy of Trace Formulas

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…

Semiclassical periodic orbit theory is used in many branches of physics. However, most applications of the theory have been to systems which involve only single particle dynamics. In this work, we develop a semiclassical formalism to…

We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…

We review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These forms provide additional insight into the…

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured…

Kraus maps (completely positive trace preserving maps) arise classically in quantum information, as they describe the evolution of noncommutative probability measures. We introduce tropical analogues of Kraus maps, obtained by replacing the…

While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…

We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…

We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…

Ray tracing algorithm simulates the physical movements of a huge amount of rays to render a high quality image, in which the tracing procedure for each ray can be implemented in parallel. By leveraging the inherent parallelism of quantum…

We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…

We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm.…

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…

We have studied two complementary decoherence measures purity and fidelity for a generic diffusive noise in two different chaotic systems (the baker and the cat maps). For both quantities, we have found classical structures in quantum…

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…

In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…

The Gutzwiller trace formula provides a semiclassical approximation for the density of states of a quantum system in terms of classical periodic orbits. In its original form Gutzwiller derived the trace formula for quantum systems without…

By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…