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. The CliNR implementation of an n-qubit Clifford circuit of size s achieves a vanishing logical error rate if snp²→ 0 where p is the physical error rate. Here, we propose a recursive version of CliNR that can reduce errors on larger circuits with a relatively small gate overhead. When np → 0, the logical error rate can be vanishingly small. This implementation requires left\(2leftlceil log(sp\)rightrceil+3right)n+1 qubits and at most 24 s leftlceil(sp)^4rightrceil gates. 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 large Clifford circuits with relatively small overheads.