Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subsystem stabilizer codes cannot have a universal set of transversal
  gates for even one encoded qudit   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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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci