Exploit fault-tolerant non-Clifford gates for code switching or magic-state injection

Determine whether the fault-tolerant non-Clifford gates provided by the singlet-only exchange-only qubit encoding can be used in code-switching or magic-state-injection protocols.

Background

The singlet-only exchange-only (SOEO) qubit supports fault-tolerant implementations of the logical gates Z_L, N_L, and M_L using auxiliary spins. Whereas Z_L is a logical Clifford operation, N_L and M_L are non-Clifford gates and are not contained in any finite level of the Clifford hierarchy. The paper notes that conventional stabilizer codes generally require magic-state injection or code switching to achieve universal fault-tolerant computation, but leaves unresolved whether the SOEO encoding’s directly available fault-tolerant non-Clifford gates can support either approach.

References

It is not yet clear if the presence of a fault-tolerant non-Clifford gate of this kind can be used for code switching or magic-state injection protocols; nevertheless, we believe this may be an interesting direction to be explored and places the SOEO qubit encoding in a unique position.

— Exchange-only qubit stabilized by a single-spin qubit  (2608.14214 - Heinz et al., 14 Aug 2026) in Section II.C, page 7

Whether magic states can more directly be injected into a PRISM code block and be distilled by its Clifford gates is open.

— Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates  (2609.37699 - Matsuura et al., 29 Sep 2026) in Section Discussion