Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of topologically protected gates for local stabilizer
  codes   Given a quantum error correcting code, an important task is to find encoded
operations that can be implemented efficiently and fault-tolerantly. In this
Letter we focus on topological stabilizer codes and encoded unitary gates that
can be implemented by a constant-depth quantum circuit. Such gates have a
certain degree of protection since propagation of errors in a constant-depth
circuit is limited by a constant size light cone. For the 2D geometry we show
that constant-depth circuits can only implement a finite group of encoded gates
known as the Clifford group. This implies that topological protection must be
"turned off" for at least some steps in the computation in order to achieve
universality. For the 3D geometry we show that an encoded gate U is
implementable by a constant-depth circuit only if the image of any Pauli
operator under conjugation by U belongs to the Clifford group. This class of
gates includes some non-Clifford gates such as the \pi/8 rotation. Our
classification applies to any stabilizer code with geometrically local
stabilizers and sufficiently large code distance.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph