Table 1 Applicability of noise shaping techniques for unitary synthesis error in single-qubit non-Clifford gates

From: Error crafting in mixed quantum gate synthesis

 

Pauli twirl

Clifford twirl

Crafting

Z rotation

Partially

Partially

✓

Arbitrary

×

×

✓

  1. Here we assume that noise shaping allows additional single-qubit Clifford gates but not non-Clifford gates. The row “Z rotation” represents the applicability of Pauli rotation gates. Here, “Partially” means that we can employ a symmetric Clifford group that commutes with the target unitary to twirl the noise within each irreducible representation. But not the entire space69,70. For instance, over- and under-rotation errors cannot be twirled; one must rely on crafting.
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