Counting, fanout and the complexity of quantum ACC
نویسندگان
چکیده
We propose definitions of QAC, the quantum analog of the classical class AC 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). This implies that QAC 0 with unbounded fanout gates, denoted QAC0wf , is the same as QACC[q] and QACC for all q. Since ACC[p] 6= ACC[q] whenever p and q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. ∗Supported in part by the NSF under grant NSF-CCR-9988310 †Supported in part by the NSF under grant NSF-PHY-0071139 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.
منابع مشابه
Quantum Circuits: Fanout, Parity, and Counting
We propose definitions of QAC, the quantum analog of the classical class AC of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], where n-ary 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 ou...
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عنوان ژورنال:
- Quantum Information & Computation
دوره 2 شماره
صفحات -
تاریخ انتشار 2002