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The quantum query complexity of certification
, 903
"... We study the quantum query complexity of finding a certificate for a dregular, klevel balanced nand formula. We show that the query complexity is ˜ Θ(d (k+1)/2) for 0certificates, and ˜ Θ(d k/2) for 1certificates. In particular, this shows that the zeroerror quantum query complexity of evaluati ..."
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We study the quantum query complexity of finding a certificate for a dregular, klevel balanced nand formula. We show that the query complexity is ˜ Θ(d (k+1)/2) for 0certificates, and ˜ Θ(d k/2) for 1certificates. In particular, this shows that the zeroerror quantum query complexity
On exact quantum query complexity
, 2011
"... We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities of pai ..."
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Cited by 3 (0 self)
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We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities
Nonadaptive quantum query complexity
, 2010
"... We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any boundederror nonadaptive quantum query algorithm that computes some total boolean function depending on n variables mu ..."
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Cited by 6 (2 self)
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We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any boundederror nonadaptive quantum query algorithm that computes some total boolean function depending on n variables
On randomized and quantum query complexities
 In preparation
, 2005
"... Abstract. We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that D(f) = O(Q1(f) 3) for any total function f, where D(f) is the minimal ..."
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Cited by 2 (0 self)
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Abstract. We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that D(f) = O(Q1(f) 3) for any total function f, where D(f) is the minimal
Quantum query complexity of state conversion
 In Proc. of 52nd IEEE FOCS
"... State conversion generalizes query complexity to the problem of converting between two inputdependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural informationtheoretic norm that extends the Schur product operator norm. The c ..."
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Cited by 35 (2 self)
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State conversion generalizes query complexity to the problem of converting between two inputdependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural informationtheoretic norm that extends the Schur product operator norm
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
Averagecase quantum query complexity
 Journal of Physics A: Mathematical and General
"... We compare classical and quantum query complexities of total Boolean functions. It has been shown that for worstcase complexity, the gap between quantum and classical can be at most polynomial [BBC + 98]. We give (nonuniform) distributions where the gap for averagecase complexity of the ORfuncti ..."
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Cited by 11 (4 self)
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We compare classical and quantum query complexities of total Boolean functions. It has been shown that for worstcase complexity, the gap between quantum and classical can be at most polynomial [BBC + 98]. We give (nonuniform) distributions where the gap for averagecase complexity of the OR
The quantum query complexity of algebraic properties
 IN PROCEEDINGS OF THE 16TH INTERNATIONAL SYMPOSIUM ON THE FUNDAMENTALS OF COMPUTATION THEORY, LECTURE NOTES IN COMPUT. SCI. 4639
, 2007
"... We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms for thes ..."
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Cited by 6 (0 self)
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We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms
Unbounded Error Quantum Query Complexity
, 2007
"... This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication complexity model, the unbounded error quantum query complexity is exa ..."
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Cited by 3 (0 self)
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This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication complexity model, the unbounded error quantum query complexity
The quantum query complexity of algebraic properties
, 2007
"... We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms for thes ..."
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Cited by 1 (0 self)
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We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms
Results 1  10
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