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555
Uselessness for an Oracle Model with Internal Randomness
, 2013
"... We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can be solved by a quantum algorithm using a single query; we sho ..."
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We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can be solved by a quantum algorithm using a single query; we
Quantum lower bounds by quantum arguments
 In Proceedings of the ACM Symposium on Theory of Computing
, 2000
"... We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a superposition of inputs. If the algorithm works correctly, its ..."
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Cited by 193 (19 self)
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We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a superposition of inputs. If the algorithm works correctly, its
Quantum walk algorithms for element distinctness
 In: 45th Annual IEEE Symposium on Foundations of Computer Science, OCT 1719, 2004. IEEE Computer Society Press, Los Alamitos, CA
, 2004
"... We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N 2/3) query quantum algorithm. This improves the previous O(N 3/4) quantum algorithm of Buhrm ..."
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Cited by 174 (13 self)
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We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N 2/3) query quantum algorithm. This improves the previous O(N 3/4) quantum algorithm
Exponential lower bound for 2query locally decodable codes via a quantum argument
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 2003
"... A locally decodable code encodes nbit strings x in mbit codewords C(x) in such a way that one can recover any bit xi from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2 classical queries require exponential length: m = 2 \Omega ( ..."
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Cited by 134 (15 self)
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A locally decodable code encodes nbit strings x in mbit codewords C(x) in such a way that one can recover any bit xi from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2 classical queries require exponential length: m = 2 \Omega
Polynomial degree vs. quantum query complexity
 Proceedings of FOCS’03
"... The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with pol ..."
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Cited by 81 (14 self)
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The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function
The quantum query complexity of approximating the median and related statistics
 STOC'99
, 1999
"... Let X = (z,, , z,,) be a sequence of n numbers. For 6> 0, we say that 5; is an eapproximate median if the number of elements strictly less than zi and the number of elements strictly greater than zi are each less than (1 + 6):. We consider the quantum query complexity of computing an capprox ..."
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Cited by 74 (1 self)
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Let X = (z,, , z,,) be a sequence of n numbers. For 6> 0, we say that 5; is an eapproximate median if the number of elements strictly less than zi and the number of elements strictly greater than zi are each less than (1 + 6):. We consider the quantum query complexity of computing an c
Quantum query complexity of some graph problems
 Proceedings of the 31st International Colloquium on Automata, Lanaguages, and Programming
, 2004
"... Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Sourc ..."
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Cited by 58 (3 self)
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Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single
Results 1  10
of
555