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Q: Quantenoptik und Photonik

Q 73: Quantencomputer

Q 73.4: Vortrag

Mittwoch, 9. März 2005, 14:45–15:00, HU 2002

Optimizing linear optics quantum gates — •Jens Eisert — Institut für Physik, Universität Potsdam, 14469 Potsdam, Germany — Blackett Laboratory, Imperial College London, London SW7 2BW, UK

In this talk, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. The success probability is a key quantity that determines on the one hand the necessary significant overhead in resources in near-deterministic quantum computation using linear optics. On the other hand, in small-scale linear optical applications one may be well-advised in any case to make use of postselected quantum gates. It is shown that by exploiting this link to convex optimization, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for linear optical networks followed by postselection, i.e., for networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a postselected non-linear sign shift gate is p=1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for linear optics quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds for elementary gates without feed-forward, although the original problem is a difficult non-convex problem in infinitely many objective variables. Similar applications of this method in finding optimal linear optical schemes are outlined.

[1] J. Eisert, quant-ph/0409156.