Some Practical Problems of Quantum Gate Teleportation (QGT)

Quantum teleportation is unquestionably an important resource, especially in the one-way computation model. However, we will focus on the circuit-based model and explore what this technique can contribute to its toolset. Quantum algorithms can benefit from teleportation if we teleport gates rather than states. This idea was investigated two decades ago by Gottesman and Chuang, whose paper optimistically claimed that teleportation is a universal computational resource.
Apart from teleporting the CX gate within the KLM protocol, though, it is hard to find convincing practical uses for this technique. Furthermore, the derivation of the CX-gate procedure itself was never fully clarified. In this talk we will revisit their method, extend it to the Toffoli gate, offer fresh motivation for pursuing gate teleportation, and identify the obstacles encountered along the way.

Plan of the talk:
1. Why we want a universal QGT procedure (spoiler: for parallel quantum computing)
2. Understanding QGT for single-qubit gates—any issues? (yes, several)
3. QGT for the CX gate—does it actually work? (more or less)
4. QGT for the Toffoli gate
5. Teleportation of several gates in a row