The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
Codes for the quan tum erasure channel
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abstract
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.
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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.
A 256-atom neutral ytterbium processor demonstrates fault-tolerant entanglement of 24 logical qubits and runs Bernstein-Vazirani on 28 logical qubits with better-than-physical error rates using erasure conversion.
citing papers explorer
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Stabilizer Codes and Quantum Error Correction
The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
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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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Fault-tolerant quantum computation with a neutral atom processor
A 256-atom neutral ytterbium processor demonstrates fault-tolerant entanglement of 24 logical qubits and runs Bernstein-Vazirani on 28 logical qubits with better-than-physical error rates using erasure conversion.