Quantum Error Correction and Orthogonal Geometry
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A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.
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Forward citations
Cited by 2 Pith papers
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The Heisenberg Representation of Quantum Computers
Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.
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Clifford Orbits from Cayley Graph Quotients
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
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