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Explore the potential of Forrelation as a candidate for demonstrating verifiable quantum advantage in this 32-minute conference talk from Quantum Industry Day 2025. Examine Aaronson's 2009 problem of determining whether a function correlates with the Fourier transform of another function, and discover its remarkable properties including its position outside the polynomial hierarchy relative to an oracle and its generalizability to BQP-complete problems. Learn why Forrelation presents an ideal test case for quantum advantage, given its simple quantum circuit implementation contrasted with exponential-time classical algorithms. Investigate proposed approaches for achieving verifiable quantum advantage through bent functions, obfuscation-like techniques, and connections to group membership problems, gaining insights into cutting-edge research at the intersection of quantum computing theory and practical quantum advantage demonstrations.
