Counting, fanout and the complexity of quantum ACC

  title={Counting, fanout and the complexity of quantum ACC},
  author={Frederic Green and Steven Homer and Cristopher Moore and Chris Pollett},
  journal={Quantum Inf. Comput.},
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 QACC[q], the analog of the class ACC[q] where Modq gates are also allowed. We prove that parity or fanout allows us to construct quantum MODq gates in constant depth for any q, so QACC [2] = QACC. More generally, we show that for any q, p > 1, MODq is equivalent to MODp (up to constant depth and polynomial size). This implies that QAC0 with… 

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