We present our last article “Data reuploading for a universal quantum classifier”, by A. PérezSalinas, A. CerveraLierta, E. GilFuster and J. I. Latorre. It is available in arXiv:1907.02085 and SciRate
The main result of this work is to show that there is a tradeoff between the number of qubits needed to perform classification and multiple data reuploading.
The quantum classifier we built can be understood as a modification of a Neural Network. In feedforward neural networks (NN), each data point is entered and processed in each neuron. If NN were affected by the nocloning theorem, they couldn’t work as they do. To build a quantum classifier (QClass), we need to load classical data several times along the computation.
To upload and process data in the QClass, we use a general unitary gate. Each of these gates (called “layer L”) introduces the data points “x” and the processing parameters “phi” that should be adjusted by using some cost function.
We train a singlequbit QClass by dividing the Bloch Sphere into several regions, one for each class, and finetune the processing parameters to distribute each data point to its corresponding region. We choose these regions to be maximally orthogonal.
Then, we can define the cost function as the fidelity of the final state of the QClass and the corresponding “class state”. We propose two ways to do that, which can be found in the article. A singlequbit QClass can’t represent any quantum advantage, although, for its simplicity, could be a part of larger circuits. However, this QClass can be generalized to multiqubit QClass, where the introduction of entanglement will improve the classification procedure. Once we have defined the QClass and the cost function, we need to use a classical minimization method to find the processing parameters. The QClass belongs to the family of parametrized quantum circuits, as the VQE or Qautoencoder. We have used the LBFGSB algorithm from scipy.
Benchmark: we have tested the single and multiqubit QClass composed by a different number of layers in several problems with different characteristics.
 Simple problem: points inside or outside of a circle. Results with a singlequbit classifier

Multidimensional problem: points inside or outside of a fourdimensional hypersphere.Singlequbit: 90% (4L), 95% (6L), 97% (8L)Twoqubit: 92% (2L), 98% (3L with entanglement)Fourqubit: 98% (2L with entanglement).

Nonconvex problem: points inside or outside of an annulus. The improvement of the QClass as we increase the number of layers is amazing!

We have also checked other problems

Finally, we have compared the performance of the singlequbit classifier with two wellknown classical classification techniques: NN and Support Vector Machines. The QClass results are comparable (sometimes better) with these methods.