Multi-class quantum classifiers with tensor network circuits for quantum phase recognition

Hybrid quantum-classical algorithms based on variational circuits are a promising approach to quantum machine learning problems for near-term devices, but the selection of the variational ansatz is an open issue. Recently, tensor network-inspired circuits have been proposed as a natural choice for such ansatz. Their employment on binary classification tasks provided encouraging results. However, their effectiveness on more difficult tasks is still unknown. In particular, the best approach to extend them to multi-class classification problems remains unclear. Here, we present numerical experiments on multi-class classifiers based on tree tensor network and multiscale entanglement renormalization ansatz circuits. We conducted experiments on image classification with the MNIST dataset and on quantum phase recognition with the XXZ model by Cirq and TensorFlow Quantum. In the former case, we reduced the number of classes to four to match the aimed output based on 2 qubits. The quantum data of the XXZ model consist of three classes of ground states prepared by a checkerboard circuit used for the ansatz of the variational quantum eigensolver, corresponding to three distinct quantum phases. Test accuracy turned out to be 59%-93% and 82%-96% respectively, depending on the model architecture and on the type of preprocessing.