Fig. 3: Performance of the network in learning the encoding channel and single qubit gates for the two-mode 5-photon χ⁽²⁾ binomial code.

a Encoding channel infidelity as a function of the depth of the network in a two-mode network. The black line indicates the infidelity of the ideally trained channel. The green and blue histograms illustrate the distribution of infidelities when splitter errors are σ = 0.001 and σ = 0.01, respectively. b Gate infidelities of single qubit logical gates (Hadamard, S and T phase gates) trained by a 4-layer network. The black bar indicates that an ideal gate can be trained to a fidelity >99.99%. The network performance is severely affected by component imperfections, with the worst-case fidelity approaching ~10%.