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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.15 No.3&4 February 2015 |
Rational approximations and quantum algorithms with postselection
(pp0295-0307)
Urmila
Mahadev and Ronald de Wolf
doi:
https://doi.org/10.26421/QIC15.3-4-5
Abstracts:
We study the close connection between rational functions
that approximate a given Boolean function, and quantum algorithms that
compute the same function using postselection. We show that the minimal
degree of the former equals (up to a factor of 2) the minimal query
complexity of the latter. We give optimal (up to constant factors)
quantum algorithms with postselection for the Majority function,
slightly improving upon an earlier algorithm of Aaronson. Finally we
show how Newman’s classic theorem about low-degree rational
approximation of the absolute-value function follows from these
algorithms.
Key words:
postselection,
Boolrean function, quantum algorithms |
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