Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit

Details Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit

2008-01-15

arxiv.org/abs/0801.2360v1

Phys. Rev. A 78, 012353 (2008)

Physics

Quantum Physics

16 pages, 3 figures

Scientific paper

10.1103/PhysRevA.78.012353

A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize our work to show that for subsystem stabilizer codes in $d$ dimensional Hilbert space, such a universal set of transversal gates cannot exist for even one encoded qudit, for any dimension $d$, prime or nonprime. This result strongly supports the idea that other primitives, such as quantum teleportation, are necessary for universal fault-tolerant quantum computation, and may be an important factor for fault tolerance noise thresholds.

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