On the Complexity of Quantum ACC

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...

• Type: Conference
• Year: 2000
• Where: COCO
• Authors: Frederic Green, Steven Homer, Chris Pollett
• Keywords: Algorithms, COCO 2000, Log-planar Qacc Operators, Qacc Operator, Quantum Gate