Quantum Stabilizer and Subsystem Codes from Algebro-geometric Toric Codes
نویسنده
چکیده
We show how to construct quantum stabilizer and subsystem codes from algebro-geometric toric codes extending the known construction of subsystem codes from cyclic codes and extending the construction of stabilizer codes from toric codes in an earlier work by one of the authors. Since algebrogeometric toric codes are higher dimensional extensions of cyclic codes, we obtain this way a new and rich source of quantum stabilizer and subsystem codes.
منابع مشابه
Quantum Stabilizer Codes from Toric Varieties
A.R. Calderbank [1], P.W. Shor [2] and A.M. Steane [3] produced quantum stabilizer codes from linear codes containing their dual codes. A. Ashikhmin, S. Litsyn and M.A. Tsfasman in [4] used the construction to obtain asymptotically good quantum codes fra codes on algebraic curves. In [5] the author developed methods to construct linear error correcting codes from toric varieties and derived the...
متن کاملEncoding Subsystem Codes
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the known results on encoding of stabilizer codes. Along the way we also show how Clifford codes can be encoded. We also show that gauge qubits can be exploited to...
متن کاملToric residue codes: I
In this paper, we begin exploring the construction of algebraic codes from toric varieties using toric residues. Though algebraic codes have been constructed from toric varieties, they have all been evaluation codes, where one evaluates the sections of a line bundle at a collection of rational points. In the present paper, instead of evaluating sections of a line bundle at rational points, we c...
متن کاملQuantum Stabilizer Codes and beyond A
Quantum Stabilizer Codes and Beyond. (August 2008) Pradeep Kiran Sarvepalli, B.Tech., Indian Institute of Technology, Madras; M.S., Texas A&M University Chair of Advisory Committee: Dr. Andreas Klappenecker The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. Despite the large body of literature in quantum coding theory, many ...
متن کاملSubsystem Codes
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the qu...
متن کامل