Synthesis of fault tolerant error correction circuits

[dsvandet]

Problem: Given a code and a set of parameters, construct a fault-tolerant error correction circuit

There are by now many ways to synthesize a fault-tolerant error correction circuit. One class of approaches measures each gauge or stabilizer generator using a separate block of ancillary qubits.

• bare circuits
• Shor circuits
• flag circuits
• ancilla-decoding circuits

Another class of approaches measures O(n-k) stabilizers in parallel.

• Steane EC (CSS codes)
• Knill EC

Recently there are also approaches that measure subsets of stabilizers in parallel.