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Artificial Orbitals and a Solution to Grover's Problem

Michael Stay
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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.

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Michael Stay. 2000-10-18. Artificial Orbitals and a Solution to Grover's Problem. https://arxiv.org/abs/quant-ph/0010065

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