# Düsseldorf 2007 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

# Q: Fachverband Quantenoptik und Photonik

## Q 57: Quanteninformation (Quantencomputer II)

### Q 57.2: Vortrag

### Donnerstag, 22. März 2007, 14:30–14:45, 5L

**Efficient algorithm for multi-qudit twirling for ensemble quantum computation** — •Geza Toth^{1} and Juan Jose Garcia-Ripoll^{2} — ^{1}Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary — ^{2}Max Planck Institute for Quantum Optics, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany

We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can also be used for computing the twirled density matrix on a classical computer. The method is based on a simple non-unitary operation involving a random unitary. When applying this basic building block iteratively, the mean squared error of the approximation decays exponentially. In contrast, when averaging over random unitary matrices the error decreases only algebraically. We present evidence that the unitaries in our algorithm can come from a very imperfect random source or can even be chosen deterministically from a set of cyclically alternating matrices. Based on these ideas we present a quantum circuit realizing twirling efficiently.