Optimal query complexity for fractional quantum evolution
The paper determines that implementing a noninteger power of an unknown unitary requires query complexity proportional to 1/(delta log 1/epsilon). This is established by constructing an upper bound using Quantum Singular Value Transformation (QSVT) and proving a matching lower bound using frequency annihilation techniques. The result shows the QSVT construction is optimal up to constant factors for approximating fractional quantum evolution.