摘要：We study stabilizer circuits that use non-stabilizer qubits and Z-measurements to produce other non-stabilizer qubits. These productions are successful when the correct measurement outcome occurs, but when the opposite outcome is observed, the non-stabilizer input qubit is potentially destroyed. In preceding work [arXiv:1803.06081 (2018)] we introduced protocols able to recreate the expensive non-stabilizer input qubit when the two-qubit stabilizer circuit has an unsuccessful measurement outcome. Such protocols potentially allow a deep computation to recover from such failed measurements without the need to repeat the whole prior computation. Possible complications arise when the recovery protocol itself suffers from a failed measurement. To deal with this, we need to use nested recovery protocols. Here we give a precise analysis of the potential advantage of such recovery protocols as we examine its optimal nesting depth. We show that if the expensive input qubit has cost d, then typically a depth O(log d) recovery protocol is optimal, while a certain special case has optimal depth O(sqrt{d}). We also show that the recovery protocol can achieve a cost reduction by a factor of at most two over circuits that do not use recovery.
关键词：stabilizer circuit; recovery circuit; magic state
