Higher Order Decompositions of Ordered Operator Exponentials

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.Comment: 16 pages, 1 figur

Quantum rejection sampling

Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of (possibly unknown) quantum states with some amplitudes, the problem is to prepare a coherent superposition of the same states, albeit with different target amplitudes. The main result of this paper is a tight characterization of the query complexity of this quantum state generation problem. We exhibit an algorithm, which we call quantum rejection sampling, and analyze its cost using semidefinite programming. Our proof of a matching lower bound is based on the automorphism principle which allows to symmetrize any algorithm over the automorphism group of the problem. Our main technical innovation is an extension of the automorphism principle to continuous groups that arise for quantum state generation problems where the oracle encodes unknown quantum states, instead of just classical data. Furthermore, we illustrate how quantum rejection sampling may be used as a primitive in designing quantum algorithms, by providing three different applications. We first show that it was implicitly used in the quantum algorithm for linear systems of equations by Harrow, Hassidim and Lloyd. Secondly, we show that it can be used to speed up the main step in the quantum Metropolis sampling algorithm by Temme et al.. Finally, we derive a new quantum algorithm for the hidden shift problem of an arbitrary Boolean function and relate its query complexity to "water-filling" of the Fourier spectrum.Comment: 19 pages, 5 figures, minor changes and a more compact style (to appear in proceedings of ITCS 2012

Multipartite Nonlocal Quantum Correlations Resistant to Imperfections

We use techniques for lower bounds on communication to derive necessary conditions in terms of detector efficiency or amount of super-luminal communication for being able to reproduce with classical local hidden-variable theories the quantum correlations occurring in EPR-type experiments in the presence of noise. We apply our method to an example involving n parties sharing a GHZ-type state on which they carry out measurements and show that for local-hidden variable theories, the amount of super-luminal classical communication c and the detector efficiency eta are constrained by eta 2^(-c/n) = O(n^(-1/6)) even for constant general error probability epsilon = O(1)

Fast motion-including dose error reconstruction for VMAT with and without MLC tracking

Multileaf collimator (MLC) tracking is a promising and clinically emerging treatment modality for radiotherapy of mobile tumours. Still, new quality assurance (QA) methods are warranted to safely introduce MLC tracking in the clinic. The purpose of this study was to create and experimentally validate a simple model for fast motion-including dose error reconstruction applicable to intrafractional QA of MLC tracking treatments of moving targets.MLC tracking experiments were performed on a standard linear accelerator with prototype MLC tracking software guided by an electromagnetic transponder system. A three-axis motion stage reproduced eight representative tumour trajectories; four lung and four prostate. Low and high modulation 6 MV single-arc volumetric modulated arc therapy treatment plans were delivered for each trajectory with and without MLC tracking, as well as without motion for reference. Temporally resolved doses were measured during all treatments using a biplanar dosimeter. Offline, the dose delivered to each of 1069 diodes in the dosimeter was reconstructed with 500 ms temporal resolution by a motion-including pencil beam convolution algorithm developed in-house. The accuracy of the algorithm for reconstruction of dose and motion-induced dose errors throughout the tracking and non-tracking beam deliveries was quantified. Doses were reconstructed with a mean dose difference relative to the measurements of-0.5% (5.5% standard deviation) for cumulative dose. More importantly, the root-mean-square deviation between reconstructed and measured motion-induced 3%/3 mm γ failure rates (dose error) was 2.6%. The mean computation time for each calculation of dose and dose error was 295 ms. The motion-including dose reconstruction allows accurate temporal and spatial pinpointing of errors in absorbed dose and is adequately fast to be feasible for online use. An online implementation could allow treatment intervention in case of erroneous dose delivery in both tracking and non-tracking treatments

Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State

The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The form of the function, though, remains as it is in the case of initial pure state. We study the role of the von Neumann entropy of the initial state, and show that the entropy cannot be a measure for the usefulness of the algorithm. We give few examples and show that for some extremely mixed initial states carrying high entropy, the generalized Grover algorithm is considerably faster than any classical algorithm.Comment: 4 pages. See http://www.cs.technion.ac.il/~danken/MSc-thesis.pdf for extended discussio

Time-resolved dose reconstruction by motion encoding of volumetric modulated arc therapy fields delivered with and without dynamic multi-leaf collimator tracking.

BACKGROUND: Organ motion during treatment delivery in radiotherapy (RT) may lead to deterioration of the planned dose, but can be mitigated by dynamic multi-leaf collimator (DMLC) tracking. The purpose of this study was to implement and experimentally validate a method for time-resolved motion including dose reconstruction for volumetric modulated arc therapy (VMAT) treatments delivered with and without DMLC tracking. MATERIAL AND METHODS: Tracking experiments were carried out on a linear accelerator (Trilogy, Varian) with a prototype DMLC tracking system. A motion stage carrying a biplanar dosimeter phantom (Delta4PT, Scandidos) reproduced eight representative clinical tumor trajectories (four lung, four prostate). For each trajectory, two single-arc 6 MV VMAT treatments with low and high modulation were delivered to the moving phantom with and without DMLC tracking. An existing in-house developed program that adds target motion to treatment plans was extended with the ability to split an arc plan into any number of sub-arcs, allowing the calculated dose for different parts of the treatment to be examined individually. For each VMAT sub-arc, reconstructed and measured doses were compared using dose differences and 3%/3 mm γ-tests. RESULTS: For VMAT sub-arcs the reconstructed dose distributions had a mean root-mean-square (rms) dose difference of 2.1% and mean γ failure rate of 2.0% when compared with the measured doses. For final accumulated doses the mean rms dose difference was 1.6% and the γ failure rate was 0.7%. CONCLUSION: The time-resolved motion including dose reconstruction was experimentally validated for complex tracking and non-tracking treatments with patient-measured tumor motion trajectories. The reconstructed dose will be of high value for evaluation of treatment plan robustness facing organ motion and adaptive RT

PENGGUNAAN MODEL PEMBELAJARAN AKTIF TEAM QUIZ DALAM MENINGKATKAN KEMAMPUAN MEMBACA PEMAHAMAN BAHASA JEPANG

Penelitian ini mengambil judul “penggunaan model pembelajaran aktif team quiz dalam meningkatkan kemampuan membaca pemahaman bahasa Jepang” . membaca pemahaman adalah memahami suatu informasi dari sebuah tulisan. membaca pemahaman merupakan salah satu pembelajaran yang sulit. Disebabkan karena metode yang digunakan oleh pengajar monoton dan kurang memotivasi siswa dalam pembelajaran membaca pemahaman. Penelitian ini bertujuan untuk mengetahui bagaimana penggunaan model pembelajaran aktif team quiz dalam meningkatkan kemampuan membaca pemahaman bahasa Jepang. Penelitian ini menggunakan metode quasi eksperiment dengan one group before-after (pretest dan posttest) design. Sampel dalam penelitian ini adalah siswa kelas XI Bahasa SMA Negeri 1 Parongpong tahun ajaran 2015/2016. Instrument penelitiannya adalah tes dan angket. Berdasarkan analisis data dengan perhitungan statistic yang menggunakan t hitung diketahui bahwa t hitung > t tabel maka Ho ditolak dan Hk diterima yang dapat disimpulkan bahwa penggunaan model pembelajaran aktif team quiz dalam meningkatkan kemampuan membaca pemahaman bahasa jepang efektif. Sedangkan hasil analisis data angket diketahui bahwa penggunaan model pembelajaran aktif team quiz dalam meningkatkan kemampuan membaca pemahaman bahasa Jepang mendapat respon positif dari siswa. ; Reading comprehension is the act of understanding information from a presented text. It is one of difficulties found in learning. It caused by monotonous method conducted by teacher and in turn, students have less motivation on learning reading comprehension. This research aims for how the Team Quiz active learning method can improve reading comprehension in Japanese. The quasi-experiment method with “one group before-after (pretest and posttest)” design is conducted in this research, by taking XI language students from 2015/2016 academic year of SMA Negeri 1 Parongpong as sample. Test and questionnaire is instrument used in this research. According to data analysis with statistical calculation using t count, noting that t count > t table, therefore Ho is rejected and Hk is accepted. To conclude, Team Quiz active learning method is effective in improving reading comprehension in Japanese. Moreover, according to data analysis conducted in questionnaire, the Team Quiz active learning method gains positive responses from students