66 research outputs found
An efficient algorithm to recognize local Clifford equivalence of graph states
In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action
of local Clifford operations on graph states in terms of a graph transformation
rule, known in graph theory as \emph{local complementation}. It was shown that
two graph states are equivalent under the local Clifford group if and only if
there exists a sequence of local complementations which relates their
associated graphs. In this short note we report the existence of a polynomial
time algorithm, published in [Combinatorica 11 (4), 315 (1991)], which decides
whether two given graphs are related by a sequence of local complementations.
Hence an efficient algorithm to detect local Clifford equivalence of graph
states is obtained.Comment: 3 pages. Accepted in Phys. Rev.
Standard Form of Qudit Stabilizer Groups
We investigate stabilizer codes with carrier qudits of equal dimension ,
an arbitrary integer greater than 1. We prove that there is a direct relation
between the dimension of a qudit stabilizer code and the size of its
corresponding stabilizer, and this implies that the code and its stabilizer are
dual to each other. We also show that any qudit stabilizer can be put in a
standard, or canonical, form using a series of Clifford gates, and we provide
an explicit efficient algorithm for doing this. Our work generalizes known
results that were valid only for prime dimensional systems and may be useful in
constructing efficient encoding/decoding quantum circuits for qudit stabilizer
codes and better qudit quantum error correcting codes.Comment: RevTeX 4.1, 6 pages, 3 tables. Any comments are welcome
Codeword Stabilized Quantum Codes
We present a unifying approach to quantum error correcting code design that
encompasses additive (stabilizer) codes, as well as all known examples of
nonadditive codes with good parameters. We use this framework to generate new
codes with superior parameters to any previously known. In particular, we find
((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding
circuits for all codes within our framework.Comment: 5 pages, 1 eps figure, ((11,48,3)) code removed, encoding circuits
added, typos corrected in codewords and elsewher
Local unitary versus local Clifford equivalence of stabilizer states
We study the relation between local unitary (LU) equivalence and local
Clifford (LC) equivalence of stabilizer states. We introduce a large subclass
of stabilizer states, such that every two LU equivalent states in this class
are necessarily LC equivalent. Together with earlier results, this shows that
LC, LU and SLOCC equivalence are the same notions for this class of stabilizer
states. Moreover, recognizing whether two given stabilizer states in the
present subclass are locally equivalent only requires a polynomial number of
operations in the number of qubits.Comment: 8 pages, replaced with published versio
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