QAC0 equals 2D geometrically local QAC0 up to quadratic blowup, while 1D local QAC0 requires nearly log or linear depth for parity depending on input placement.
[Ber11] Debajyoti Bera
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On the Computational Complexity of Geometrically Local QAC0 circuits
QAC0 equals 2D geometrically local QAC0 up to quadratic blowup, while 1D local QAC0 requires nearly log or linear depth for parity depending on input placement.