Parity vs. AC0 with Simple Quantum Preprocessing

Watch a technical conference talk from TQC 2024 exploring the limitations of quantum preprocessing in computing parity functions. Delve into research investigating whether AC0◦QNC0 (a hybrid circuit model combining constant-depth quantum computation with classical AC0 circuits) can effectively compute or correlate with parity functions. Learn about key findings that demonstrate negligible correlation between ancilla-free QNC0 circuits and parity, even with sophisticated post-processing. Examine the relationship between quantum preprocessing and Boolean function decision tree complexity, revealing that nonlocal channels offer no advantages over randomness in this context. Understand how these results suggest that while QNC0 shows promise for search and sampling tasks, its power remains inaccessible to simple classical computation when solving decision problems. The presentation was delivered at the 19th Conference on the Theory of Quantum Computation, Communication and Cryptography, hosted at the Okinawa Institute for Science and Technology.