Extended Data Fig. 6: Bell state error correction from all the error subspaces.
From: Quantum error detection in a silicon quantum processor
a, Experimental circuit used to recover \(| {\Phi }^{+}\rangle\) from the four error subspaces. This is realised by preparing \(\frac{1}{\sqrt{2}}(| {\Downarrow \Downarrow \rangle} +| {\Downarrow \Uparrow \rangle} )=\frac{1}{2}(| {\Phi }^{+}\rangle +| {\Phi }^{-}\rangle +| {\Psi }^{+}\rangle +| {\Psi }^{-}\rangle )\), which is an equal superposition of the four Bell states. Quantum state tomography is then performed on the data qubits corresponding to different error syndromes, where nearly equal probabilities are observed for the four possible measurement outcomes of the syndromes: {0,0}, {0,1}, {1,0}, and {1,1}. The data qubits are mapped to corresponding Bell state with fidelities of \({F}_{| {\Phi }^{+}\rangle }=81.6\pm 2.6 \% ,{F}_{| {\Psi }^{+}\rangle }=80.6\pm 2.7 \% ,{F}_{| {\Phi }^{-}\rangle }=75.7\pm 2.8 \%\), and \({F}_{| {\Psi }^{-}\rangle }=80.4\pm 2.9 \%\), respectively, as illustrated in b-e. Based on the error syndromes, the error state ρerror can be corrected by applying a corresponding single-qubit operation U through ρcorrect = UρerrorU† by postprocessing. As shown in f, \(| {\Phi }^{+}\rangle\) is finally recovered with a fidelity of \({F}_{| {\Phi }^{+}\rangle }=79.0\pm 1.4 \%\).
