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COCO

2000

Springer

2000

Springer

For any q > 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t > 1, MODq is equivalent to MODt (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC(0) , ACC[q], and ACC, denoted QAC (0) wf , QACC[2], QACC respectively, deﬁne the same class of operators, leaving q > 2 as an open question. Our result resolves this question, proving that QAC (0) wf = QACC[q] = QACC for all q. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We deﬁne classes of languages EQACC, NQACC and BQACCQ. We deﬁne a notion of log-planar QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in P/poly. We also deﬁne a notion of log-gate restricted QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in TC(0) . To do this last proof, we show that TC(0) c...

Related Content

Added |
02 Aug 2010 |

Updated |
02 Aug 2010 |

Type |
Conference |

Year |
2000 |

Where |
COCO |

Authors |
Frederic Green, Steven Homer, Chris Pollett |

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