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Magic states were introduced in the context of Clifford circuits as aresource that elevates classically simulatable computations to quantumuniversal capability, while maintaining the same gate set. Here we study magicstates in the context of matchgate (MG) circuits, where the notion becomes moresubtle, as MGs are subject to locality constraints and also the SWAP gate isnot available. Nevertheless a similar picture of gate-gadget constructionsapplies, and we show that every pure fermionic state which is non-Gaussian,i.e. which cannot be generated by MGs from a computational basis state, is amagic state for MG computations. This result has significance for prospectivequantum computing implementation in view of the fact that MG circuit evolutionscoincide with the quantum physical evolution of non-interacting fermions.

All pure fermionic non-Gaussian states are magic states for matchgate computations