Posted

Ewin Tang, John Wright (Aug 01 2025).
Abstract: We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude estimation, assume the ability to apply a state preparation unitary UU and its inverse UU^\dagger; we give problem instances based on trace estimation where no algorithm which uses only UU beats the naive, quadratically slower approach. Our proof of this is simple and goes through the compressed oracle method introduced by Zhandry. Since these two subroutines are responsible for the ubiquity of the quadratic "Grover" speedup in quantum algorithms, our result explains why such speedups are far harder to come by in the settings of quantum learning, metrology, and sensing. In these settings, UU models the evolution of an experimental system, so implementing UU^\dagger can be much harder -- tantamount to reversing time within the system. Our result suggests a dichotomy: without inverse access, quantum speedups are scarce; with it, quantum speedups abound.

Order by:

Want to join this discussion?

Join our community today and start discussing with our members by participating in exciting events, competitions, and challenges. Sign up now to engage with quantum experts!