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arxiv quant-ph/0409116 v3 pith:FCR2QFCA submitted 2004-09-17 quant-ph

All Quantum Adversary Methods are Equivalent

classification quant-ph
keywords adversarymethodquantumequivalentknownmethodsweightedalgorithms
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary (Ambainis, 2003), strong weighted adversary (Zhang, 2005), and the Kolmogorov complexity adversary (Laplante and Magniez, 2004). We also pa few new equivalent formulations of the method. This shows that there is essentially _one_ quantum adversary method. From our approach, all known limitations of these versions of the quantum adversary method easily follow.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A Quantum Algorithm for Finding $k$-Minima

    quant-ph 2019-07 unverdicted novelty 4.0

    Quantum algorithm for k-minima with O(sqrt(k N)) query complexity via threshold search and generalized amplitude amplification.