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This paper introduces a generalization of perfect state transfer in continuous time quantum walks on graph and explores basic properties and example of this phenomenon. 

ABSTRACT We report on the discovery of Gliese 12 b, the nearest transiting temperate, Earth-sized planet found to date. Gliese 12 is a bright (V = 12.6 mag, K = 7.8 mag) metal-poor M4V star only 12.162 ± 0.005 pc away from the Solar system with one of the lowest stellar activity levels known for M-dwarfs. A planet candidate was detected by TESS based on only 3 transits in sectors 42, 43, and 57, with an ambiguity in the orbital period due to observational gaps. We performed follow-up transit observations with CHEOPS and ground-based photometry with MINERVA-Australis, SPECULOOS, and Purple Mountain Observatory, as well as further TESS observations in sector 70. We statistically validate Gliese 12 b as a planet with an orbital period of 12.76144 ± 0.00006 d and a radius of 1.0 ± 0.1 R⊕, resulting in an equilibrium temperature of ∼315 K. Gliese 12 b has excellent future prospects for precise mass measurement, which may inform how planetary internal structure is affected by the stellar compositional environment. Gliese 12 b also represents one of the best targets to study whether Earth-like planets orbiting cool stars can retain their atmospheres, a crucial step to advance our understanding of habitability on Earth and across the galaxy. 

ABSTRACT We report the discovery of a warm sub-Saturn, TOI-257b (HD 19916b), based on data from NASA’s Transiting Exoplanet Survey Satellite (TESS). The transit signal was detected by TESS and confirmed to be of planetary origin based on radial velocity observations. An analysis of the TESS photometry, the Minerva-Australis, FEROS, and HARPS radial velocities, and the asteroseismic data of the stellar oscillations reveals that TOI-257b has a mass of MP = 0.138 ± 0.023 $$\rm {M_J}$$ (43.9 ± 7.3 $$\, M_{\rm \oplus}$$), a radius of RP = 0.639 ± 0.013 $$\rm {R_J}$$ (7.16 ± 0.15 $$\, \mathrm{ R}_{\rm \oplus}$$), bulk density of $$0.65^{+0.12}_{-0.11}$$ (cgs), and period $$18.38818^{+0.00085}_{-0.00084}$$ $$\rm {days}$$. TOI-257b orbits a bright (V = 7.612 mag) somewhat evolved late F-type star with M* = 1.390 ± 0.046 $$\rm {M_{sun}}$$, R* = 1.888 ± 0.033 $$\rm {R_{sun}}$$, Teff = 6075 ± 90 $$\rm {K}$$, and vsin i = 11.3 ± 0.5 km s−1. Additionally, we find hints for a second non-transiting sub-Saturn mass planet on a ∼71 day orbit using the radial velocity data. This system joins the ranks of a small number of exoplanet host stars (∼100) that have been characterized with asteroseismology. Warm sub-Saturns are rare in the known sample of exoplanets, and thus the discovery of TOI-257b is important in the context of future work studying the formation and migration history of similar planetary systems.