Approximating Hamiltonian dynamics with the Nyström method

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nyström method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations

Detection of an atmosphere around the super-Earth 55 Cancri e

We report the analysis of two new spectroscopic observations of the super-Earth 55 Cancri e, in the near infrared, obtained with the WFC3 camera onboard the HST. 55 Cancri e orbits so close to its parent star, that temperatures much higher than 2000 K are expected on its surface. Given the brightness of 55 Cancri, the observations were obtained in scanning mode, adopting a very long scanning length and a very high scanning speed. We use our specialized pipeline to take into account systematics introduced by these observational parameters when coupled with the geometrical distortions of the instrument. We measure the transit depth per wavelength channel with an average relative uncertainty of 22 ppm per visit and find modulations that depart from a straight line model with a 6$\sigma$ confidence level. These results suggest that 55 Cancri e is surrounded by an atmosphere, which is probably hydrogen-rich. Our fully Bayesian spectral retrieval code, T-REx, has identified HCN to be the most likely molecular candidate able to explain the features at 1.42 and 1.54 $\mu$m. While additional spectroscopic observations in a broader wavelength range in the infrared will be needed to confirm the HCN detection, we discuss here the implications of such result. Our chemical model, developed with combustion specialists, indicates that relatively high mixing ratios of HCN may be caused by a high C/O ratio. This result suggests this super-Earth is a carbon-rich environment even more exotic than previously thought.Comment: 10 pages, 10 figures, 4 tables, Accepted for publication in Ap

A population study of gaseous exoplanets

We present here the analysis of 30 gaseous extrasolar planets, with temperatures between 600 and 2400 K and radii between 0.35 and 1.9 $R_\mathrm{Jup}$. The quality of the HST/WFC3 spatially scanned data combined with our specialized analysis tools allow us to study the largest and most self-consistent sample of exoplanetary transmission spectra to date and examine the collective behavior of warm and hot gaseous planets rather than isolated case-studies. We define a new metric, the Atmospheric Detectability Index (ADI) to evaluate the statistical significance of an atmospheric detection and find statistically significant atmospheres around 16 planets out of the 30 analysed. For most of the Jupiters in our sample, we find the detectability of their atmospheres to be dependent on the planetary radius but not on the planetary mass. This indicates that planetary gravity plays a secondary role in the state of gaseous planetary atmospheres. We detect the presence of water vapour in all of the statistically detectable atmospheres, and we cannot rule out its presence in the atmospheres of the others. In addition, TiO and/or VO signatures are detected with 4$\sigma$ confidence in WASP-76 b, and they are most likely present in WASP-121 b. We find no correlation between expected signal-to-noise and atmospheric detectability for most targets. This has important implications for future large-scale surveys.Comment: 14 pages, 12 figures, 3 tables, published in A

Experimental learning of quantum states

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales

Transiting Exoplanet Studies and Community Targets for JWST's Early Release Science Program

The James Webb Space Telescope will revolutionize transiting exoplanet atmospheric science due to its capability for continuous, long-duration observations and its larger collecting area, spectral coverage, and spectral resolution compared to existing space-based facilities. However, it is unclear precisely how well JWST will perform and which of its myriad instruments and observing modes will be best suited for transiting exoplanet studies. In this article, we describe a prefatory JWST Early Release Science (ERS) program that focuses on testing specific observing modes to quickly give the community the data and experience it needs to plan more efficient and successful future transiting exoplanet characterization programs. We propose a multi-pronged approach wherein one aspect of the program focuses on observing transits of a single target with all of the recommended observing modes to identify and understand potential systematics, compare transmission spectra at overlapping and neighboring wavelength regions, confirm throughputs, and determine overall performances. In our search for transiting exoplanets that are well suited to achieving these goals, we identify 12 objects (dubbed "community targets") that meet our defined criteria. Currently, the most favorable target is WASP-62b because of its large predicted signal size, relatively bright host star, and location in JWST's continuous viewing zone. Since most of the community targets do not have well-characterized atmospheres, we recommend initiating preparatory observing programs to determine the presence of obscuring clouds/hazes within their atmospheres. Measurable spectroscopic features are needed to establish the optimal resolution and wavelength regions for exoplanet characterization. Other initiatives from our proposed ERS program include testing the instrument brightness limits and performing phase-curve observations.(Abridged)Comment: This is a white paper that originated from an open discussion at the Enabling Transiting Exoplanet Science with JWST workshop held November 16 - 18, 2015 at STScI (http://www.stsci.edu/jwst/science/exoplanets). Accepted for publication in PAS

ExoClock Project: An open platform for monitoring the ephemerides of Ariel targets with contributions from the public

The Ariel mission will observe spectroscopically around 1000 exoplanets to further characterise their atmospheres. For the mission to be as efficient as possible, a good knowledge of the planets' ephemerides is needed before its launch in 2028. While ephemerides for some planets are being refined on a per-case basis, an organised effort to collectively verify or update them when necessary does not exist. In this study, we introduce the ExoClock project, an open, integrated and interactive platform with the purpose of producing a confirmed list of ephemerides for the planets that will be observed by Ariel. The project has been developed in a manner to make the best use of all available resources: observations reported in the literature, observations from space instruments and, mainly, observations from ground-based telescopes, including both professional and amateur observatories. To facilitate inexperienced observers and at the same time achieve homogeneity in the results, we created data collection and validation protocols, educational material and easy to use interfaces, open to everyone. ExoClock was launched in September 2019 and now counts over 140 participants from more than 15 countries around the world. In this release, we report the results of observations obtained until the 15h of April 2020 for 119 Ariel candidate targets. In total, 632 observations were used to either verify or update the ephemerides of 83 planets. Additionally, we developed the Exoplanet Characterisation Catalogue (ECC), a catalogue built in a consistent way to assist the ephemeris refinement process. So far, the collaborative open framework of the ExoClock project has proven to be highly efficient in coordinating scientific efforts involving diverse audiences. Therefore, we believe that it is a paradigm that can be applied in the future for other research purposes, too

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio

The composition of a disrupted extrasolar planetesimal at SDSS J0845+2257 (Ton 345)

We present a detailed study of the metal-polluted DB white dwarf SDSS J0845+2257 (Ton 345). Using high-resolution Hubble Space Telescope/Cosmic Origins Spectrograph and Very Large Telescope spectroscopy, we have detected hydrogen and 11 metals in the atmosphere of the white dwarf. The origin of these metals is almost certainly the circumstellar disc of dusty and gaseous debris from a tidally disrupted planetesimal, accreting at a rate of 1.6 × 1010 g s−1. Studying the chemical abundances of the accreted material demonstrates that the planetesimal had a composition similar to the Earth, dominated by rocky silicates and metallic iron, with a low water content. The mass of metals within the convection zone of the white dwarf corresponds to an asteroid of at least ∼130–170 km in diameter, although the presence of ongoing accretion from the debris disc implies that the planetesimal was probably larger than this. While a previous abundance study of the accreted material has shown an anomalously high mass fraction of carbon (15 per cent) compared to the bulk Earth, our independent analysis results in a carbon abundance of just 2.5 per cent. Enhanced abundances of core material (Fe, Ni) suggest that the accreted object may have lost a portion of its mantle, possibly due to stellar wind stripping in the asymptotic giant branch. Time series spectroscopy reveals variable emission from the orbiting gaseous disc, demonstrating that the evolved planetary system at SDSS J0845+2257 is dynamically active

Observing Exoplanets with the James Webb Space Telescope

The census of exoplanets has revealed an enormous variety of planets or- biting stars of all ages and spectral types: planets in orbits of less than a day to frigid worlds in orbits over 100 AU; planets with masses 10 times that of Jupiter to planets with masses less than that of Earth; searingly hot planets to temperate planets in the Habitable Zone. The challenge of the coming decade is to move from demography to physical characterization. The James Webb Space Telescope (JWST) is poised to open a revolutionary new phase in our understanding of exoplanets with transit spectroscopy of relatively short period planets and coronagraphic imaging of ones with wide separations from their host stars. This article discusses the wide variety of exoplanet opportunities enabled by JWSTs sensitivity and stability, its high angular resolution, and its suite of powerful instruments. These capabilities will advance our understanding of planet formation, brown dwarfs, and the atmospheres of young to mature planets