Extended Data Fig. 6: Extended binomial QPT data.

For each panel, we plot the process matrix in the Pauli transfer representation (bottom) and a reconstructed state represented in the Pauli basis (top). For the reconstructed state, we choose the input state \((| 0\rangle +| 1\rangle )| 0\rangle /\sqrt{2}\), which should result in the Bell state \(| {\Phi }^{+}\rangle =(| 00\rangle +| 11\rangle )/\sqrt{2}\) when the CNOT gate is applied. The ideal process for each panel is represented by the dominant components taken to ±1 and small components taken to 0. a, Conditioned QPT results when the feedforward operations are not applied. The first four panels (labelled ‘00’, ‘01’, ‘10’ and ‘11’) represent the processes conditioned on measurement outcome. Each has qualitatively the same features (for example, the same non-zero elements of the process matrix); however, the differing signs between the four outcomes indicate that each process is modified by single-qubit operations. When all measurement results are combined (labelled ‘All’), most of the features are washed away and only certain Pauli operators are left invariant by the process: {II, IX, ZI, ZX}. These operators are exactly the feedforward operations that would normally be applied. This behaviour can also be observed in the state tomography results (top), in which each measurement outcome heralds a different Bell state (\(\{| {\Psi }^{+}\rangle ,| {\Psi }^{-}\rangle ,| {\Phi }^{+}\rangle ,| {\Phi }^{-}\rangle \}\)); when taken all together, the states add incoherently, resulting in a completely mixed state. b, Conditioned QPT results when the feedforward operations are applied. Here, all measurement outcomes (00, 01, 10, 11) indicate the same process, that of the CNOT process. Therefore, when the measurement outcomes are all taken together (All), the compiled process is that of a CNOT gate.