Handling Leakage with Subsystem Codes

The distance-3 and distance-5 rotated subsystem surface codes.  Although the weight-6 rectangular stabilizers are larger than the weight-4 stabilizer of the surface code, they can be measured in pairs of triangular gauge operators.  This locality limits correlated errors due to leakage, resulting in 0.75x less data qubits required for fault-tolerance in a damaging ion-trap leakage model. 


When building a quantum computer, the very first thing you need are qubits.  These are encodings of quantum information into two distinguished levels of a quantum mechanical system.  When your system is subjected to noise, it can either perturb your information within these two distinguished levels, or send your information to other parts of the system.  When these levels are preserved, quantum error-correction can do an excellent job of also preserving your information.  When they are not, we say that your qubit is leaked, and error-correction can struggle to fix the problem.

In this work, we identify codes that are well-suited to handle these leakage events.  The idea is simple: you can trade error-corrective performance within the distinguished levels for error-corrective performance outside the distinguished levels.  This manifests as trading parity checks, which give information about errors within the distinguished levels, for locality, which ensures that leaked qubits can’t propagate too many errors.  With this intuition, we identify subsystem surface codes and Bacon-Shor codes as encodings that offer good performance in the presence of highly damaging leakage.  For more details see our preprint arXiv:1903.03937.