Scaling of running time of quantum adiabatic algorithm for propositional satisfiability

We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially with their size. Worst case complexity of quantum adiabatic algorithm therefore seems to be exponential.Comment: 7 page

Exponential complexity of an adiabatic algorithm for an NP-complete problem

We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to the ground state. For large problem sizes the gap decreases exponentially and as a consequence the required running time is also exponential.Comment: 5 pages, 2 figures; v3. published versio

Optimal parametrizations of adiabatic paths

The parametrization of adiabatic paths is optimal when tunneling is minimized. Hamiltonian evolutions do not have unique optimizers. However, dephasing Lindblad evolutions do. The optimizers are simply characterized by an Euler-Lagrange equation and have a constant tunneling rate along the path irrespective of the gap. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing. Dephasing rates that beat Grover imply hidden resources in Lindblad operators.Comment: 4 pages, 2 figures; To prevent from misunderstanding, we clarified the discussion of an apparent speedup in the Grover algorithm; figures improved + minor change

Human-induced changes in Indonesian peatlands increase drought severity

Indonesian peatlands are critical to the global carbon cycle, but they also support a large number of local economies. Intense forest clearing and draining in these peatlands is causing severe ecological and environmental impacts. Most studies highlighted increased carbon emission in the region through drought and large-scale fires, further accelerating peatland degradation. Yet, little is known about the long-term impacts of human-induced disturbance on peatland hydrology in the tropics. Here we show that converting natural peat forests to plantations can significantly alter the hydrological system far worse than previously recognized, leading to amplified moisture stress and drought severity. This study quantified how human-induced changes to Indonesian peatlands have affected drought severity. Through field observations and modelling, we demonstrate that canalization doubled drought severity; logging and starting plantations even quadrupled drought severity. Recognizing the importance of peatlands to Indonesia, proper management, and rehabilitating peatlands remain the only viable option for continued plantation use

Excitation-Dependent Photoluminescence from Single-Carbon Dots

Carbon dots (CDs) are carbon-based fluorescent nanoparticles that can exhibit excitation-dependent photoluminescence (PL) “tunable” throughout the entire visible range, interesting for optoelectronic and imaging applications. The mechanism underlying this tunable emission remains largely debated, most prominently being ascribed to dot-to-dot variations that ultimately lead to excitation-dependent ensemble properties. Here, single-dot spectroscopy is used to elucidate the origin of the excitation-dependent PL of CDs. It is demonstrated that already single CDs exhibit excitation-dependent PL spectra, similar to those of the CD ensemble. The single dots, produced by a facile one-step synthesis from chloroform and diethylamine, exhibit emission spectra with several characteristic peaks differing in emission peak position and spectral width and shape, indicating the presence of distinct emission sites on the CDs. Based on previous work, these emission sites are related to the sp2 subregions in the carbon core, as well as the functional groups on the surface. These results confirm that it is possible to integrate and engineer different types of electronic transitions at the nanoscale on a single CD, making these CDs even more versatile than organic dyes or inorganic quantum dots and opening up new routes toward light-emission engineering

An Upper Mass Limit on a Red Supergiant Progenitor for the Type II-Plateau Supernova SN 2006my

We analyze two pre-supernova (SN) and three post-SN high-resolution images of the site of the Type II-Plateau supernova SN 2006my in an effort to either detect the progenitor star or to constrain its properties. Following image registration, we find that an isolated stellar object is not detected at the location of SN 2006my in either of the two pre-SN images. In the first, an I-band image obtained with the Wide-Field and Planetary Camera 2 on board the Hubble Space Telescope, the offset between the SN 2006my location and a detected source ("Source 1") is too large: > 0.08", which corresponds to a confidence level of non-association of 96% from our most liberal estimates of the transformation and measurement uncertainties. In the second, a similarly obtained V-band image, a source is detected ("Source 2") that has overlap with the SN 2006my location but is definitively an extended object. Through artificial star tests carried out on the precise location of SN 2006my in the images, we derive a 3-sigma upper bound on the luminosity of a red supergiant that could have remained undetected in our pre-SN images of log L/L_Sun = 5.10, which translates to an upper bound on such a star's initial mass of 15 M_Sun from the STARS stellar evolutionary models. Although considered unlikely, we can not rule out the possibility that part of the light comprising Source 1, which exhibits a slight extension relative to other point sources in the image, or part of the light contributing to the extended Source 2, may be due to the progenitor of SN 2006my. Only additional, high-resolution observations of the site taken after SN 2006my has faded beyond detection can confirm or reject these possibilities.Comment: Minor text changes from Version 1. Appendix added detailing the determination of confidence level of non-association of point sources in two registered astronomical image

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure