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We study quantum algorithms on search trees of unknown structure, in a model where the tree can be discovered by local exploration.
M. Davis and H. Putnam. A computing procedure for quantification theory. Journal of the ACM
1960
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M. Davis, G. Logemann, and D. Loveland. A machine program for theorem proving. Communications of the ACM
1962
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Uniform random spanning trees
R. Pemantle · 1995
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L. K. Grover. A fast quantum mechanical algorithm for database search. Proceedings of the ACM Symposium on the Theory of Computing (STOC’1996)
1996
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Random walks on graphs: A survey
L. Lovász · 1996
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Lectures on contemporary probability
G. F. Lawler, L. N. Coyle · 1999
Cited alongside, same era.
M. Szegedy. Quantum speed-up of Markov chain based algorithms. Proceedings of FOCS’2004
2004
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E. Farhi, J. Goldstone, S. Gutman, A quantum algorithm for the Hamiltonian NAND tree. Theory of Computing
2008
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Matrix mathematics. Theory, facts, and formulas
D. S. Bernstein · 2009
Cited alongside, same era.
Markov chains and mixing times. With a chapter by James G. Propp and David B. Wilson
D. A. Levin, Y. Peres, E. L. Wilmer · 2009
Cited alongside, same era.
Quantum walk speedup of backtracking algorithms
A. Montanaro
Cited in the paper.
A. Ambainis, A. Childs, B. Reichardt, R. Špalek, S. Zhang. 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. SIAM Journal on Computing
2010
Later among the works it cites.
B. Reichardt. Faster quantum algorithm for evaluating game trees. Proceedings of SODA’2011
2011
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Matrix analysis
R. A. Horn, C. R. Johnson · 2012
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Probability on trees and networks
R. Lyons, Y. Peres · 2016
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