Fig. 1: Adaptive boson sampling, tailored for quantum machine learning, via measurement post-selection.
From: Quantum machine learning with Adaptive Boson Sampling via post-selection
a The algorithm aims at solving a binary classification problem: in a 2D plane filled with different shapes, the goal is to classify the items according to the color feature. b Each point of the dataset is encoded in a quantum state \(\vert {\psi }_{{{\boldsymbol{p}}}}\rangle\), according to the optical circuit output mode, with which such state is triggered. Actually, in the ABS theoretical scheme, the detection of a photon, exiting from U0, in one of the lower modes determines a specific adaptive transformation Up that cooperates in the generation of the state \(\vert {\psi }_{{{\boldsymbol{p}}}}\rangle\). c The dataset is classified using a kernel method, specifically a Support Vector Machine. The kernel elements, defined as the overlap square moduli, can be directly derived from the sketched linear optical circuit, in which Vp is composed of U0 and Up. The square modulus of the overlap can be experimentally obtained through a measurement post-selection of the fraction of coincidences in which photons leave the circuit from the same modes as they entered. d Another way to evaluate the kernel arises from a post-selection reconstruction of the states with a tomography protocol, exploiting the projective unitary T that acts on the adaptive modes. This is the case of the experiment we implement here. After that, the kernel is provided to a classical hardware, which manages the binary classification task.
