Fault-tolerant syndrome extraction can be compressed from r stabilizer measurements to O(d log r) by combining stabilizer generators through the parity check matrix of a classical code.
A Note on Quantum Hamming Bound
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Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length of single and double error-correcting MDS stabilizer codes over finite fields.
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Compressing Syndrome Measurement Sequences
Fault-tolerant syndrome extraction can be compressed from r stabilizer measurements to O(d log r) by combining stabilizer generators through the parity check matrix of a classical code.