Efficient Computations of Encodings for Quantum Error Correction
نویسندگان
چکیده
We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists of O(nd) operations, and converts k-qubit data (where k = n − d) into n-qubit codewords. 02.70.Rw, 03.65.Bz, 89.80.+h Typeset using REVTEX ∗[email protected] †[email protected]
منابع مشابه
Eecient Computations of Encodings for Quantum Error Correction Typeset Using Revt E X
We show how, given any set of generators of the stabilizer of a quantum code, an eecient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists of O(nd) operations, and converts k-qubit data (where k = n ? d) into n-qubit codewords.
متن کاملEfficient one-way quantum computations for quantum error correction
A method is presented for the implementation of edge local complementation (ELC) in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme for constructing a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of ELCs. A single physi...
متن کاملQuantum Error-Correction Codes on Abelian Groups
We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.
متن کاملGENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...
متن کاملCombined error correction techniques for quantum computing architectures
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we m...
متن کامل