It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speed-up of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.
@article{arxiv.quant-ph/0401066,
title = {Charge detection enables free-electron quantum computation},
author = {C. W. J. Beenakker and D. P. DiVincenzo and C. Emary and M. Kindermann},
journal= {arXiv preprint arXiv:quant-ph/0401066},
year = {2007}
}