Abstract
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speedup. The search for new quantum algorithms benefits from understanding their limitations: Some tasks are impossible in quantum circuits, although their classical versions are easy, for example, cloning. An example with a unitary oracle is the if clause, the task to implement controlled (up to the phase on ). In classical computation the conditional statement is easy and essential. In quantum circuits the if clause was shown impossible from one query to . Is it possible from polynomially many queries? Here we unify algorithms with a unitary oracle and develop a topological method to prove their limitations: No number of queries to and lets quantum circuits implement the if clause, even if admitting approximations, postselection, and relaxed causality. We also show limitations of process tomography, oracle neutralization, and , and algorithms. Our results strengthen an advantage of linear optics, challenge the experiments on relaxed causality, and motivate new algorithms with many-outcome measurements.
2 More- Received 9 November 2023
- Revised 10 January 2024
- Accepted 29 February 2024
DOI:https://doi.org/10.1103/PhysRevA.109.032625
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society