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Non-binary Unitary Error Bases and Quantum Codes

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arxiv quant-ph/9608048 v2 pith:4MOJXPJF submitted 1996-08-29 quant-ph

Non-binary Unitary Error Bases and Quantum Codes

classification quant-ph
keywords codeserrorbasesquantumbasisconstructionabelianallow
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed from linear codes over $\ints_n$ for any $n$. The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.

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Cited by 6 Pith papers

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