期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1999
卷号：1999
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We propose definitions of \QAC0, the quantum analog of the
classical class \AC0 of constant-depth circuits with AND and OR
gates of arbitrary fan-in, and \QACC0[q], the analog of the class
\ACC0[q] where \Modq gates are also allowed. We show that it is
possible to make a `cat' state on n qubits in constant depth if and
only if we can construct a parity or \Mod2 gate in constant depth;
therefore, any circuit class that can fan out a qubit to n copies in
constant depth also includes \QACC0[2]. In addition, we prove the
somewhat surprising result that parity or fanout allows us to
construct \Modq gates in constant depth for any q, so \QACC0[2]=\QACC0. Since \ACC0[p]=\ACC0[q] whenever p and q are
distinct primes, \QACC0[2] is strictly more powerful than its
classical counterpart, as is \QAC0 when fanout is allowed.
