Fast optimization of parametrized quantum optical circuits

Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the infinite dimensionality of the photon number vector space that is associated to each optical mode. Truncating the space dimension is unavoidable, and it can lead to incorrect results if the gates populate photon number states beyond the cutoff. To tackle this issue, we present an algorithm that is orders of magnitude faster than the current state of the art, to recursively compute the exact matrix elements of Gaussian operators and their gradient with respect to a parametrization. These operators, when augmented with a non-Gaussian transformation such as the Kerr gate, achieve universal quantum computation. Our approach brings two advantages: first, by computing the matrix elements of Gaussian operators directly, we don't need to construct them by combining several other operators; second, we can use any variant of the gradient descent algorithm by plugging our gradients into an automatic differentiation framework such as TensorFlow or PyTorch. Our results will find applications in quantum optical hardware research, quantum machine learning, optical data processing, device discovery and device design.Comment: 21 pages, 10 figure

A New Light Particle in B Decays?

We investigate the possibility whether the tensions with SM expectations observed in several b -> sll transitions, including hints for lepton flavour non-universality, could be due to the decay of B into a new light resonance. We find that qualitative agreement with the data can be obtained with a light vector resonance dominantly decaying invisibly. This scenario predicts a shift in the muon anomalous magnetic moment that could explain the long-standing discrepancy. The most stringent constraint comes from searches for B decays with missing energy. A striking prediction is a strong q^2 dependence of the lepton flavour universality ratios R_K and R_K* that should allow to clearly confirm or rule out this possibility experimentally. We also comment on the possible connection of the invisible decay product with Dark Matter.Comment: 5 pages, 2 figures. v2: typos corrected, references and clarifications adde

An end-to-end-construction for singly periodic minimal surfaces

We show the existence of various families of properly embedded singly periodic minimal surfaces in R^3 with finite arbitrary genus and Scherk type ends in the quotient. The proof of our results is based on the gluing of small perturbations of pieces of already known minimal surfaces.Comment: 49 page

Full characterization of the quantum spiral bandwidth of entangled biphotons

Spontaneous parametric down-conversion has been shown to be a reliable source of entangled photons. Among the wide range of properties shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum, l, and radial momentum, p, of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: l, p, and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived

Hamiltonians for one-way quantum repeaters

Quantum information degrades over distance due to the unavoidable imperfections of the transmission channels, with loss as the leading factor. This simple fact hinders quantum communication, as it relies on propagating quantum systems. A solution to this issue is to introduce quantum repeaters at regular intervals along a lossy channel, to revive the quantum signal. In this work we study unitary one-way quantum repeaters, which do not need to perform measurements and do not require quantum memories, and are therefore considerably simpler than other schemes. We introduce and analyze two methods to construct Hamiltonians that generate a repeater interaction that can beat the fundamental repeaterless key rate bound even in the presence of an additional coupling loss, with signals that contain only a handful of photons. The natural evolution of this work will be to approximate a repeater interaction by combining simple optical elements.Comment: 8 pages, 3 figure

Noise-robust quantum sensing via optimal multi-probe spectroscopy

The dynamics of quantum systems are unavoidably influenced by their environment and in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.Comment: 13 pages, 14 figure

Simultaneous intensive photometry and high resolution spectroscopy of Delta Scuti stars. V. The high--degree modes in the pulsational content of BV Circini

We discuss here the pulsation properties of the $\delta$ Scuti star BV Circini on the basis of data obtained during a simultaneous photometric and spectroscopic campaign in 1996 and a spectroscopic one in 1998, and taking also advantage of the previous photometric observations by Kurtz (1981). Nine pulsation modes were detected from photometry and thirteen from spectroscopy; five of them are in common to both techniques. The spectroscopic data give ample evidence of dramatic amplitude variations in some modes, in particular the strongest spectroscopic mode in 1998 was not detectable in 1996 data. The two dominant photometric modes (6.33 and 7.89 c\d) are observed on both seasons. The typing of the modes was performed by means of a simultaneous model fit of line profile and light variations. The 6.33 c\d photometric term is probably the fundamental radial mode, while the 7.89 c\d is a nonradial mode with mi different than 0. There are six high-degree prograde modes with an azimuthal order m ranging from -12 to -14, and also a retrograde mode with m~7. These modes combined with the identification of the 6.33 c\d mode allowed us to estimate i~60 deg for the value of the inclination of the rotation axis. An accurate evaluation of the main stellar physical parameters is also proposed as a result of the pulsational analysis.Comment: 12 pages (in A&A style), 9 ps figures (Fig. 7 in colour) Accepted for A&A Main Journa