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## "Quantum Teleportation is a Universal Computational Primitive", Daniel Gottesman, Isaac Chuang, 1999

*Reviewed August 25, 2023*

*Citation:* Gottesman, Daniel, and Isaac L. Chuang. "Quantum teleportation is a universal computational primitive." arXiv preprint quant-ph/9908010 (1999).

*Web:* https://arxiv.org/abs/quant-ph/9908010

*Tags:* Abelian-anyons, Computer-scientific

This paper discusses how to perform universal quantum computation with well-chosen ancillias. That is, how one can use measurements to "teleport" high-quality entanglement from the ancillias to the qubits in order to apply gates. By applying Pauli corrections, one can do every Clifford gate with this method. Using Clifford corrections, one can do every gate on the next level of the Clifford hierarchy.

In fact, this is the paper which introduces the Clifford hierarchy, and motivates why it is useful. Using teleportation, and can inductively construct elements of the next level of the hierarchy from the previous one.

One potential application listed is that the quantum Fourier transform on n bits is in the nth level of the hierarchy, so a linear number of these steps can get you to Fourier transform.

The nice thing about this procedure is that it is "fault tolerant", in the sense that if you can do Paulis perfectly and you can prepare the states perfectly then all of this goes through without any errors. Of course, this pushes the problem back to how to prepare these magic states, which one does through magic state distillation:

> Bravyi, Sergey, and Alexei Kitaev. "Universal quantum computation with ideal Clifford gates and noisy ancillas." Physical Review A 71.2 (2005): 022316.