Related papers: Quantum chaos with graphs: a silicon photonics pla…

Wave-particle duality, intertwining two inherently contradictory properties of quantum systems, remains one of the most conceptually profound aspects of quantum mechanics. By using the concept of energy capacity, the ability of a quantum…

We prove an analogue of the pointwise Weyl law for families of unitary matrices obtained from quantization of one-dimensional interval maps. This quantization for interval maps was introduced by Pako\'nski et al. [J. Phys. A: Math. Gen. 34…

Strong light-matter coupling between a guided electromagnetic mode and an excitonic semiconductor transition gives rise to exciton-polaritons with optical nonlinearities far exceeding those of conventional photonic platforms. Utilizing…

In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral…

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this…

We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…

Following an idea by Joyner et al. [EPL, 107 (2014) 50004] a microwave graph with antiunitary symmetry T obeying T^2=-1 has been realized. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a…

We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al.…

Quantum technologies have become a powerful paradigm for quantum information and simulation, while quantum chaos plays a key role in understanding complex quantum dynamics. Integrated photonics offers unique advantages for quantum…

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,…

Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…

We apply the scattering matrix formalism to wave mixing on a quantum two-level system. We carry out the fermionization of the two-level system degrees of freedom using the Popov-Fedotov semions, calculate n-particle Green's function, and…

We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erd\H{o}s-R\'enyi graphs using probes scalable on near-term quantum devices. By tuning the graph connectivity, the system exhibits a crossover…

Future quantum computers require a scalable architecture on a scalable technology---one that supports millions of high-performance components. Measurement-based protocols, based on graph states, represent the state of the art in…

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…

We demonstrate the existence of chaotic geodesics for the Einstein-Rosen standing gravitational waves. The complex dynamics of massive test particles are governed by a chaotic heteroclinic network. We present the fractal associated with the…

The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…

We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z)$, which we take to be ergodic. Under some natural…