The 2D HLF problem lies in QNC^0 but not in AC^0, with an exponential average-case correlation lower bound against AC^0 circuits.
Terhal and David P
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Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits
The 2D HLF problem lies in QNC^0 but not in AC^0, with an exponential average-case correlation lower bound against AC^0 circuits.