Extended Data Fig. 4: Two qubit gate implemented in two modes of a single trapped ion.
From: Encoding a qubit in a trapped-ion mechanical oscillator
This circuit implements \({\hat{\sigma }}_{L}^{i}\)-controlled \(\pm {\hat{\sigma }}_{L}^{j}\) operations between two grid state qubits \(\left|{Q}_{1}\right\rangle \) and \(\left|{Q}_{2}\right\rangle \) mediated by one internal ancillary qubit \(\left|0\right\rangle \leftrightarrow \left|1\right\rangle \). The required operations are shown in the left circuit, while on the right the equivalent logical operation is shown. The sign of the operation is determined by the ancillary qubit readout. See Methods for details.
