370 research outputs found
Provable Advantage for Quantum Strategies in Random Symmetric XOR Games
No full textNon-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of n players with 0-1 valued questions. For this class of games, each player receives an input bit and responds with an output bit without communicating to the other players. The winning condition only depends on XOR of output bits and is constant w.r.t. permutation of players. We prove that for almost any n-player symmetric XOR game the entangled value of the game is Theta((sqrt(ln(n)))/(n^{1/4})) adapting an old result by Salem and Zygmund on the asymptotics of random trigonometric polynomials. Consequently, we show that the classical-quantum gap is Theta(sqrt(ln(n))) for almost any symmetric XOR game
Exact Quantum Query Complexity of EXACT and THRESHOLD
No full textA quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we present two new exact quantum algorithms for natural problems:
- for the problem EXACT_k^n in which we have to determine whether the sequence of input bits x_1, ..., x_n contains exactly k values x_i=1;
- for the problem THRESHOLD_k^n in which we have to determine if at least k of n input bits are equal to 1
Dr. Michael Janis, Morehouse College, August 2011, August 2011
No full textThis video is a conversation with Dr. Michael Janis. Dr. Janis talks about his book, "Africa After Modernism: Transitions in Literature, Media and Philosophy". Yolanda Gilmore-Bivins, AUC Woodruff Library, is the interviewer
Polynomials, Quantum Query Complexity, and Grothendieck's Inequality
No full textWe show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function f is computable by a 1-query quantum algorithm with error bounded by epsilon<1/2 iff f can be approximated by a degree-2 polynomial with error bounded by epsilon'<1/2. This result holds for two different notions of approximation by a polynomial: the standard definition of Nisan and Szegedy and the approximation by block-multilinear polynomials recently introduced by Aaronson and Ambainis [Aaronson/Ambainis, STOC 2015]. The proof uses Grothendieck's inequality to relate two matrix norms, with one norm corresponding to polynomial approximations and the other norm corresponding to quantum algorithms.
We also show two results for polynomials of higher degree. First, there is a total Boolean function which requires ~Omega(n) quantum queries but can be represented by a block-multilinear polynomial of degree ~O(sqrt(n)). Thus, in the general case (for an arbitrary number of queries), block-multilinear polynomials are not equivalent to quantum algorithms.
Second, for any constant degree k, the two notions of approximation by a polynomial (the standard and the block-multilinear) are equivalent. As a consequence, we solve an open problem from [Aaronson/Ambainis, STOC 2015], showing that one can estimate the value of any bounded degree-k polynomial p:{0,1}^n -> [-1,1] with O(n^{1-1/(2k)) queries
Janis Hutchinson oral history interview and transcript
No full textThis recording and transcript form part of a collection of oral history interviews conducted by Center for the Study of Women, Gender, and Sexuality at Rice University. This collection includes video recordings and transcripts of interviews with Houstonians who have made contributions to the LGBT community.Dr. Janis Hutchinson is a professor in the Department of Anthropology at the University of Houston. She is a medicial anthropologist, specializing in health issues among peoples of color. She is the author of numerous journal articles and has been collecting oral histories in the African American community among African American lesbians
Dimtris 17
No full textJanis "John" Dimitris with his Boy Scout troop in the Geestadth displaced persons camp, Germany, 1946
Dimitris 28
No full textScrapbook information about Latvian military honours and awards, collected by Janis Dimitris
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