Artificial Orbitals and a Solution to Grover's Problem
arXiv:quant-ph/0010065
Abstract
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.
To distinguish the two eigenvectors, one has to distinguish their energies, but the gap is exponentially small