Between Shor and Steane: A unifying construction for measuring error syndromes

Understand

Fault-tolerant quantum error correction requires the measurement of error syndromes in a way that minimizes correlated errors on the quantum data.

• Steane and Shor ancilla are two well-known methods for fault-tolerant syndrome extraction.
• In this paper, we find a unifying construction that generates a family of ancilla blocks that interpolate between Shor and Steane.
• This family increases the complexity of ancilla construction in exchange for reducing the rounds of measurement required to fault-tolerantly measure the error.