# Quantum counterfeit coin problems

@inproceedings{Iwama2010QuantumCC,
title={Quantum counterfeit coin problems},
author={Kazuo Iwama and Harumichi Nishimura and Raymond H. Putra and Junichi Teruyama},
booktitle={Theor. Comput. Sci.},
year={2010}
}
• Published in Theor. Comput. Sci. 2 September 2010
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## References

SHOWING 1-10 OF 32 REFERENCES
Lower bounds for randomized and quantum query complexity using Kolmogorov arguments
• Computer Science, Mathematics
Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
• 2004
A very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply, and derives a general form of the ad hoc weighted method used by Hoyer, Neerbek and Shi to give a quantum lower bound on ordered search and sorting.
Reflections for quantum query algorithms
We show that any boolean function can be evaluated optimally by a quantum query algorithm that alternates a certain fixed, input-independent reflection with a second reflection that coherently
Symmetry-Assisted Adversaries for Quantum State Generation
• Computer Science, Mathematics
2011 IEEE 26th Annual Conference on Computational Complexity
• 2011
A new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem and answer an open question due to Spalek by showing that the multiplicative version of the adversary method is stronger than the additive one for any problem.
• Computer Science, Mathematics
STOC '07
• 2007
A stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function, and which is a lower bound on bounded-error quantum query complexity.
Quantum query complexity and semi-definite programming
• Computer Science
18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.
• 2003
A general lower bound for quantum query complexity is derived that encompasses a lower bound method of Ambainis and its generalizations and an interpretation of a generalized form of branching in quantum computation.
Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function
• B. Reichardt
• Computer Science
2009 50th Annual IEEE Symposium on Foundations of Computer Science
• 2009
It is generally that properties of eigenvalue-zero eigenvectors in fact imply an "effective" spectral gap around zero, and a strong universality result for span programs follows.
Quantum Query Complexity of State Conversion
• Computer Science, Mathematics
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
• 2011
It is obtained that the general adversary bound characterizes the quantum query complexity of any function whatsoever, implying that discrete and continuous-time query models are equivalent in the bounded-error setting, even for the general state-conversion problem.
Quantum complexity theory
• Computer Science
STOC '93
• 1993
This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.
A fast quantum mechanical algorithm for database search
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .