Recursive Clifford Noise Reduction 

Clifford noise reduction  (CliNR) is a partial error correction scheme that reduces the logical error rate of Clifford circuits at the cost of a modest qubit  and gate overhead.

Here, we propose recursive version of CliNR that has better performance when the circuits are very large. For an n-qubit Clifford of size s implemented with noise rate p, recursive CliNR can achive a vanishing logical error rate as long as np → 0. The implementation has a size overhead that's  at most quartic in sp. 

Using numerical simulations, we show that the recursive method can offer an advantage in a realistic near-term parameter regime. When circuit sizes are large enough, recursive CliNR can reach a lower logical error rate than the original CliNR with the same gate overhead.  The results offer promise for reducing logical errors in quantum circuits with large Clifford blocks.