Quantum Oracle Interrogation: Getting All Information for Almost Half the Price

Consider a quantum computer in combination with a binary oracle of domain size N . It is shown how N/2 + √ N calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+ √ N queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2 + O( √ N) oracle queries. In the second part of the article ‘approximate interrogation’ is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio. ∗ c ©1998 IEEE. Published in the Proceedings of FOCS’98, 8-11 November 1998 in Palo Alto, CA. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works, must be obtained from the ieee. Contact: Manager, Copyrights and Permissions/ieee Service Center/ 445 Hoes Lane/P.O. Box 1331 / Piscataway, NJ 08855-1331, USA. Telephone: +Intl. 732-562-3966.