Handbook for Efficiently Quantifying Robustness of Magic

The nonstabilizerness, or magic, is an essential quantum resource to perform universal quantum computation. Robustness of magic (RoM) in particular characterizes the degree of usefulness of a given quantum state for non-Clifford operation. While the mathematical formalism of RoM can be given in a concise manner, it is extremely challenging to determine the RoM in practice, since it involves superexponentially many pure stabilizer states. In this work, we present efficient novel algorithms to compute the RoM. The crucial technique is a subroutine that achieves the remarkable features in calculation of overlaps between pure stabilizer states: (i) the time complexity per each stabilizer is reduced exponentially, (ii) the space complexity is reduced superexponentially. Based on this subroutine, we present algorithms to compute the RoM for arbitrary states up to $n=7$ qubits on a laptop, while brute-force methods require a memory size of 86 TiB. As a byproduct, the proposed subroutine allows us to simulate the stabilizer fidelity up to $n=8$ qubits, for which naive methods require memory size of 86 PiB so that any state-of-the-art classical computer cannot execute the computation. We further propose novel algorithms that utilize the preknowledge on the structure of target quantum state such as the permutation symmetry of disentanglement, and numerically demonstrate our state-of-the-art results for copies of magic states and partially disentangled quantum states. The series of algorithms constitute a comprehensive ``handbook'' to scale up the computation of the RoM, and we envision that the proposed technique applies to the computation of other quantum resource measures as well.Comment: 16+12 pages, 8+1 figure

Use of EO-1 Hyperion Data for Inter-Sensor Calibration of Vegetation Indices

Numerous satellite sensor systems useful in terrestrial Earth observation and monitoring have recently been launched and their derived products are increasingly being used in regional and global vegetation studies. The increasing availability of multiple sensors offer much opportunity for vegetation studies aimed at understanding the terrestrial carbon cycle, climate change, and land cover conversions. Potential applications include improved multiresolution characterization of the surface (scaling); improved optical-geometric characterization of vegetation canopies; improved assessments of surface phenology and ecosystem seasonal dynamics; and improved maintenance of long-term, inter-annual, time series data records. The Landsat series of sensors represent one group of sensors that have produced a long-term, archived data set of the Earth s surface, at fine resolution and since 1972, capable of being processed into useful information for global change studies (Hall et al., 1991)

THE ENERGY CONVERSION EFFICIENCY OF DRIVER SHOT IN FEMALE PROFESSIONAL AND AMATEUR GOLFERS

The purpose of this study was to evaluate the performance of driver shot from the viewpoint of the energy conversion efficiency between club head and ball at impact. Six female professional golfers and six female amateur golfers participated in this study. All subjects were instructed to hit a straight ball with their usual swing. Each subject performed ten trials. Three dimensional coordinates of reflective markers attached on a body and club landmarks were obtained using the motion capture system operating at 250 Hz. High speed camera was used to measure the movement of the club head and ball. The energy conversion efficiency was significantly different between professional and amateur golfers (

A New Method of Microcatheter Heat-Forming for Cerebral Aneurysmal Coiling Using Stereolithography Three-Dimensional Printed Hollow Vessel Models

[Background] To perform successful coil embolization of cerebral aneurysms, it is crucial to make an appropriately shaped microcatheter tip for an aneurysm and its parent artery. So far, we manually shaped a mandrel by referencing two-dimensional (2D) images of a rotation digital subtraction angiography (DSA) on a computer screen. However, this technique requires a lot of experience, and often involves trial and error. Recently, there have been increasing reports of manual mandrel shaping using a full-scale three-dimensional (3D) model of an aneurysm and its parent artery output by various types of 3D printer. We have further developed this method by producing a hollow model of an aneurysm and its parent artery with a stereolithography 3D printer and inserting a mandrel inside the model to fit and stabilize a microcatheter tip. [Methods] Based on digital imaging and communications in medicine (DICOM) data obtained by rotational DSA, 3D images of an aneurysm and its parent artery were created and converted into standard triangulated language (STL) data. A hollow model was produced by extruding the STL data outward in the normal direction, and then a hole was made at the tip of the aneurysm using these STL data. We output these STL data to a stereolithography 3D printer. After cleaning and sterilizing the model, the mandrel was inserted in the direction of the parent artery through the hole made in the tip of the aneurysm and pushed in, creating the ideal mandrel shape. Twelve cases (14 aneurysms) were included in this study. A microcatheter tip was shaped by this method for patients who were scheduled to undergo coil embolization for an unruptured aneurysm. [Results] In 13 of the 14 aneurysms, the microcatheter was easily guided into the aneurysms in one or two trials, the position of the microcatheter tip in the aneurysm was appropriate, and the stability during coil embolization was high. [Conclusion] Our method differs from the conventional one in that a hollow model made of resin is produced with a stereolithography 3D printer and that the mandrel is shaped by inserting it retrogradely into the hollow model. Using our new method, it will be possible to shape the tip of a microcatheter suitable for safe and stable coil embolization without relying on an operator’s experience