Abstract
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form where is an unknown (normalized) state. The problem is to produce by adding a Hamiltonian (independent of and evolving the system. If is chosen uniformly at random we can (with high probability) produce in a time proportional to . If is instead chosen from a fixed, known orthonormal basis we can also produce in a time proportional to and we show that this time is optimally short. This restricted problem is an analog analogue to Grover’s algorithm, a computation on a conventional (!) quantum computer that locates a marked item from an unsorted list of items in a number of steps proportional to .
- Received 11 December 1996
DOI:https://doi.org/10.1103/PhysRevA.57.2403
©1998 American Physical Society