Grover Algorithm with zero theoretical failure rate

In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by two phase rotation through angle $\phi$. The rotation angle is given analytically to be $\phi=2 \arcsin(\sin{\pi\over (4J+6)}\over \sin\beta)$, where $\sin\beta={1\over \sqrt{N}}$, $N$ the number of items in the database, and $J$ an integer equal to or greater than the integer part of $({\pi\over 2}-\beta)/(2\beta)$. Upon measurement at $(J+1)$-th iteration, the marked state is obtained with certainty.Comment: 5 pages. Accepted for publication in Physical Review

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

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

Necessary Condition for the Quantum Adiabatic Approximation

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also give a necessary condition for the adiabatic approximation that depends on local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur

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

Fetching marked items from an unsorted database in NMR ensemble computing

Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.Comment: 4 pages and 1 figur

Neutralisation of uPA with a Monoclonal Antibody Reduces Plasmin Formation and Delays Skin Wound Healing in tPA-Deficient Mice

Background: Proteolytic degradation by plasmin and metalloproteinases is essential for epidermal regeneration in skin wound healing. Plasminogen deficient mice have severely delayed wound closure as have mice simultaneously lacking the two plasminogen activators, urokinase-type plasminogen activator (uPA) and tissue-type plasminogen activator (tPA). In contrast, individual genetic deficiencies in either uPA or tPA lead to wound healing kinetics with no or only slightly delayed closure of skin wounds. Methodology/Principal Findings: To evaluate the therapeutic potential in vivo of a murine neutralizing antibody directed against mouse uPA we investigated the efficacy in skin wound healing of tPA-deficient mice. Systemic administration of the anti-mouse uPA monoclonal antibody, mU1, to tPA-deficient mice caused a dose-dependent delay of skin wound closure almost similar to the delayed kinetics observed in uPA;tPA double-deficient mice. Analysis of wound extracts showed diminished levels of plasmin in the mU1-treated tPA-deficent mice. Immunohistochemistry revealed that fibrin accumulated in the wounds of such mU1-treated tPA-deficent mice and that keratinocyte tongues were aberrant. Together these abnormalities lead to compromised epidermal closure. Conclusions/Significance: Our findings demonstrate that inhibition of uPA activity with a monoclonal antibody in adult tPA-deficient mice mimics the effect of simultaneous genetic ablation of uPA and tPA. Thus, application of the murin

On continuous variable quantum algorithms for oracle identification problems

We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation between the continuous representation and its Fourier-transform dual representation, the corresponding Deutsch-Jozsa algorithm is probabilistic hence forbids an exponential speed-up, contrary to a previous claim in the literature.Comment: RevTeX4, 15 pages with 10 figure

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

Quantum Algorithms for the Most Frequently String Search, Intersection of Two String Sequences and Sorting of Strings Problems

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the string that occurs in the sequence most often. We propose a quantum algorithm that has a query complexity $\tilde{O}(n \sqrt{k})$. This algorithm shows speed-up comparing with the deterministic algorithm that requires $\Omega(nk)$ queries. The second one is searching intersection of two sequences of strings. All strings have the same length $k$. The size of the first set is $n$ and the size of the second set is $m$. We propose a quantum algorithm that has a query complexity $\tilde{O}((n+m) \sqrt{k})$. This algorithm shows speed-up comparing with the deterministic algorithm that requires $\Omega((n+m)k)$ queries. The third problem is sorting of $n$ strings of length $k$. On the one hand, it is known that quantum algorithms cannot sort objects asymptotically faster than classical ones. On the other hand, we focus on sorting strings that are not arbitrary objects. We propose a quantum algorithm that has a query complexity $O(n (\log n)^2 \sqrt{k})$. This algorithm shows speed-up comparing with the deterministic algorithm (radix sort) that requires $\Omega((n+d)k)$ queries, where $d$ is a size of the alphabet.Comment: THe paper was presented on TPNC 201