Error mitigation for universal gates on encoded qubits

Understand

The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates.

• For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such as the T-gate, to achieve universality.
• Common methods to implement fault-tolerant T-gates like magic state distillation generate a significant hardware overhead that will likely prevent their practical usage in the near-term future.
• Recently methods have been developed to mitigate the effect of noise in shallow quantum circuits that are not protected by error correction.