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We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks.
A fast quantum mechanical algorithm for database search
L. K. Grover · 1996
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Tight bounds on quantum searching
M. Boyer, G. Brassard, P. Høyer, and A. Tapp · 1998
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Quantum lower bounds by quantum arguments
A. Ambainis · 2000
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Quantum lower bounds by polynomials
R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf · 2001
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Quantum random-walk search algorithm
N. Shenvi, J. Kempe, and K. B. Whaley · 2003
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Quantum walk algorithm for element distinctness
A. Ambainis · 2004
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Quantum lower bounds for the collision and element distinctness problems
S. Aaronson and Y. Shi · 2004
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Quantum speed-up of Markov chain based algorithms
M. Szegedy · 2004
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Quantum algorithms for Element Distinctness
H. Buhrman, C. Dürr, M. Heiligman, P. Høyer, M. Santha, F. Magniez, and R. de Wolf · 2005
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Quantum verification of matrix products
H. Buhrman and R. Špalek · 2006
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Quantum algorithms for the triangle problem
F. Magniez, M. Santha, and M. Szegedy · 2007
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Quantum complexity of testing group commutativity
A. Nayak and F. Magniez · 2007
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Span programs and quantum query complexity: The general adversary bound is nearly tight for every Boolean function
B. Reichardt · 2009
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Any AND-OR formula of size N N can be evaluated in time N 1 / 2 + o ( 1 ) N^{1/2+o(1)} on a quantum computer
A. Ambainis, A. M. Childs, B. W. Reichardt, R. Špalek, and S. Zhang · 2010
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Quantum algorithm for k-distinctness with prior knowledge on the input
A. Belovs and T. Lee · 2011
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Quantum query complexity of minor-closed graph properties
Search via quantum walk
F. Magniez, A. Nayak, J. Roland, and M. Santha · 2011
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Reflections for quantum query algorithms
B. Reichardt · 2011
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Quantum query of subgraph containment with constant-sized certificates, 2011
Y. Zhu · 2011
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Learning-graph-based quantum algorithm for k-distinctness
A. Belovs · 2012
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Span programs for functions with constant-sized 1-certificates
A. Belovs · 2012
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Span programs and quantum algorithms for st-connectivity and claw detection
A. Belovs and B. Reichardt · 2012
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A. Childs and R. Kothari · 2011
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Random Graphs
S. Janson, T. Luczak, and A. Rucinski · 2011
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Quantum query complexity of state conversion
T. Lee, R. Mittal, B. Reichardt, R. Spalek, and M. Szegedy · 2011
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A learning graph based quantum query algorithm for finding constant-size subgraphs
T. Lee, F. Magniez, and M. Santha · 2011
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Improved output-sensitive quantum algorithms for Boolean matrix multiplication
F. Le Gall · 2012
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On the hitting times of quantum versus random walks
F. Magniez, A. Nayak, P. Richter, and M. Santha · 2012
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Improved quantum query algorithms for triangle finding and associativity testing
T. Lee, F. Magniez, and M. Santha · 2013
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