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Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

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Reports tagged with adversary method:
TR03-005 | 28th December 2002
Scott Aaronson

Quantum Certificate Complexity

Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation ... more >>>

TR10-110 | 14th July 2010
Ben Reichardt

Span programs and quantum query algorithms

Quantum query complexity measures the number of input bits that must be read by a quantum algorithm in order to evaluate a function. Hoyer et al. (2007) have generalized the adversary semi-definite program that lower-bounds quantum query complexity. By giving a matching algorithm, we show that the general adversary lower ... more >>>

TR10-191 | 9th December 2010
Andris Ambainis, Loïck Magnin, Martin Roetteler, Jérémie Roland

Symmetry-assisted adversaries for quantum state generation

We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum ... more >>>

TR12-117 | 17th September 2012
Loïck Magnin, Jérémie Roland

Explicit relation between all lower bound techniques for quantum query complexity

The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending ... more >>>

ISSN 1433-8092 | Imprint