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Non-binary Unitary Error Bases and Quantum Codes
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Non-binary Unitary Error Bases and Quantum Codes
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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.
Forward citations
Cited by 2 Pith papers
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Noise-Directed Adaptive Remapping for Integer Optimization: from qubits to (encoded) qudits
Extends NDAR to integer domains via gauge transformations, analyzes encoding tradeoffs on Max-k-colorable subgraph, and proposes noise as a new encoding selection criterion.
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Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory
Introduces hybrid Clifford codes by extending representation-theoretic quantum error correction to hybrid classical-quantum information and projective representations using the operator algebra framework.
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