Measurement-free code-switching for low overhead quantum computation using permutation invariant codes

Understand

Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem.

• Existing solutions like gate teleportation and magic state distillation are resource-intensive.
• We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabiliser code for transversal Cliffords and a permutation-invariant (PI) code for transversal non-Cliffords that are logical $Z$ rotations for any rational multiple of $\pi$.
• The novel non-Clifford gates enabled by this code-switching protocol provide for a lower gate count implementation of a universal gate set relative to the Clifford$+T$ gate set.