Hamiltonian Oracles

摘要

Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In addition to being a potentially useful tool in the study of standard oracles, Hamiltonian oracles naturally introduce the concept of fractional queries and are amenable to study using techniques of differential equations and differential geometry. As an example of these ideas we examine the Hamiltonian oracles corresponding to the problem of oracle interrogation and the problem of computing the XOR of the hidden bits. We derive lower bounds for these problems and show their relation to the study of geodesics on spheres with non-round metrics.