Artificial Orbitals and a Solution to Grover's Problem
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.
Cite
@article{arxiv.quant-ph/0010065,
title = {Artificial Orbitals and a Solution to Grover's Problem},
author = {Michael Stay},
journal= {arXiv preprint arXiv:quant-ph/0010065},
year = {2021}
}
Comments
To distinguish the two eigenvectors, one has to distinguish their energies, but the gap is exponentially small