  By allowing measurements of observables other than the state of the qubits in
a quantum computer, one can find eigenvectors very quickly. If a unitary
operation U is implemented as a time-independent Hamiltonian, for instance, one
can collapse the state of the computer to a nearby eigenvector of U with a
measurement of the energy. We examine some recent proposals for quantum
computation using time-independent Hamiltonians and show how to convert them
into ``artificial orbitals'' whose energy eigenstates match those of U. This
system can be used to find eigenvectors and eigenvalues with a single
measurement. We apply this technique to Grover's algorithm and the continuous
variant proposed by Farhi and Gutmann.

Quantum Physics