Phase Classification through Hybrid Learning in the NISQ Era

Lode Pollet  (LMU)

Over the years our group has developed a machine learning algorithm suitable for phase classification. The framework builds on a support vector machine based on tensorial kernels (TKSVM). It has the additional advantage that it can be made quasi-unsupervised in combination with graph theory. This is leveraged, in combination with the strong interpretability properties of TKSVM, to detect (novel) phases of classical matter in a typical research setting consisting of rather few data of noisy quality. Recently, we have extended the algorithm so that it becomes suitable for the post-processing of quantum data. In particular, experimental data on trapped ions from the University of Innsbruck have been successfully classified, discriminating between a trivial paramagnetic phase and a symmetry protected phase characterized by string order. The precise form of the string correlators could be inferred, and interpreted. This was demonstrated for the cluster Hamiltonian with spin-1/2 qubits, as well as for Haldane order with spin-1 particles, implemented with both qubits and qutrits.  Our hybrid approach paves the way to classify data of future quantum experiments with many qubits in regimes where no classical algorithms are feasible.