Figure 4
In the synergic quantum generative learning protocol, the probability of jointly postselecting the listed states is proportional to the value of the cost function (14). This means that the cost function reaches its maximum value if both the discriminator and the generator perform their tasks optimally. (a) State \(|\lambda \rangle\) labels the class of the output of a generator. It is a control state that is not changed by the operation of source \({\mathscr {R}}\) or generator \({\mathscr {G}}.\) For a classical label \(\lambda ,\) circuit (a) can be replaced with (b). In panel (c) we demonstrate an equivalent circuit inspired by a SWAP test36, where the measured quantity depends only on the rate of the projections of the first and the last qubits. Note that in the case of QGAN, in contrast to the synergic approach, one has to build (i) a circuit that compares \({\mathscr {R}}\) with \({\mathscr {G}}\), (ii) a circuit that evaluates the performance of \({\mathscr {D}}\) on \({\mathscr {R}},\) and (iii) a circuit that evaluates the performance of \({\mathscr {D}}\) on \({\mathscr {G}}.\) To compare SQGEN with QGAN we also include the bottom qubit in all the panels is measured in Z basis. Depending on the outcome, we include or ignore the existence of \({\mathscr {D}}.\) This allows to measure either the cost function or only source-generator fidelity. No hyperparamters are set by trial of error.
