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Abstract: This paper addresses the question of understanding quantum algorithms in terms of unitary operators. Many quantum algorithms can be expressed as applications of operators formed by conjugating so-called classical operators. The operators that are used for conjugation are determined by the problem and any additional structure possessed by the Hilbert space that is acted upon. We prove many new commutative laws between these different operators, and we use those to phrase and analyze old and new... (Update)
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...is only quadratic. Some other quantum algorithms that are naturally expressed in the black box model are described in [10, 4, 19, 5, 6, 17, 22, 9, 7, 21, 8]. Of course, upper bounds in the black box model immediately yield upper bounds for the circuit description model in...
...6. Output a = sin 2 ( y M ) Steps 1 to 5 are illustrated on Figure 1. This algorithm can also be summarized, following the approach in [11], as the unitary transformation (F 1 M I) M (Q) FM I) applied on state j0iAj0i, followed by a measurement of the rst register and...
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BibTeX entry: (Update)
P. Høyer. Conjugated operators in quantum algorithms. Preprint, 1997. http://citeseer.ist.psu.edu/102581.html More
@misc{ hoyer97conjugated,
author = "P. Hoyer",
title = "Conjugated operators in quantum algorithms",
text = "P. Høyer. Conjugated operators in quantum algorithms. Preprint, 1997.",
year = "1997",
url = "citeseer.ist.psu.edu/102581.html" }
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