Tree-tensor-network classifiers for machine learning: From quantum inspired to quantum assisted

作者：Michael L. Wall, Giuseppe D’Aguanno · 发表于：Physical Review A · 年份：2021 · DOI：10.1103/physreva.104.042408 · 被引用次数：32 · 研究领域：Quantum Computing Algorithms and Architecture、Quantum many-body systems、Quantum Information and Cryptography

We describe a quantum-assisted machine learning method in which multivariate data are encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree-tensor-network (TTN) topology acting as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion and then applying a supervised linear classifier encoding the class decision in a small-dimensional quantum register. We present tools for making TTN classifiers amenable to implementation on gate-based quantum computing devices, including an embedding map with accuracy similar to the recently defined exponential machines (A. Novikov et al., arXiv:1605.03795) but which produces valid quantum state embeddings of classical data vectors, and the use of manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights a...