Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries

Understand

Quantum error correction and symmetries play central roles in quantum information science and physics.

• It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot correct erasure errors perfectly (a well-known result in this regard being the Eastin-Knill theorem in the context of fault-tolerant quantum computing), in contrast to the case without symmetry constraints.
• Furthermore, several quantitative fundamental limits on the accuracy of such covariant codes for approximate quantum error correction are known.
• Here, we consider the quantum error correction capability of uniformly random covariant codes.