Tree-tensor-network classifiers for machine learning: From quantum inspired to quantum assisted
چکیده
We describe a quantum-assisted machine learning method in which multivariate data are encoded into quantum states Hilbert space whose dimension is exponentially large the length of vector. Learning this occurs through applying low-depth circuit with tree-tensor-network (TTN) topology acting as an unsupervised feature extractor to identify most relevant data-driven fashion and then supervised linear classifier encoding class decision small-dimensional register. present tools for making TTN classifiers amenable implementation on gate-based computing devices, including embedding map accuracy similar recently defined exponential machines (A. Novikov et al., arXiv:1605.03795) but produces valid state embeddings classical vectors, use manifold-based gradient optimization schemes produce isometric operations mapping register qubits defining decision. detail methods efficiently obtaining one-point two-point correlation functions vectors boundary model, can be used model interpretability, well classification decisions from partial vectors. Further, we show that tensors significantly aid human interpretability extracted weights may models less susceptible adversarial perturbations. Finally, discuss problem compiling classically optimized unitary run computers how requiring postselection hardware precondition variational Ans\"atze without postselection. demonstrate our methodologies applications utilizing MNIST database handwritten digits time-series set activity recognition.