Abstract There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer.Abstract There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer.

Machine Learning Science and TechnologyMar 1, 20242 citations

Quantum Supervised Learning

Antonio Macaluso

arXiv:2407.17161Künstliche Intell.Jul 19, 20248 citations

A hybrid quantum-classical classifier based on branching multi-scale entanglement renormalization ansatz

Yanyan Hou, Jian Li, Xiu‐Bo Chen +1 more

Label propagation is an essential semi-supervised learning method based on graphs, which has a broad spectrum of applications in pattern recognition and data mining. This paper proposes a quantum semi-supervised classifier based on label propagation. Considering the difficulty of graph construction, we develop a variational quantum label propagation (VQLP) method. In this method, a locally parameterized quantum circuit is created to reduce the parameters required in the optimization. Furthermore, we design a quantum semi-supervised binary classifier based on hybrid Bell and $Z$ bases measurement, which has shallower circuit depth and is more suitable for implementation on near-term quantum devices. We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set, and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier. This work opens a new path to quantum machine learning based on graphs.Label propagation is an essential semi-supervised learning method based on graphs, which has a broad spectrum of applications in pattern recognition and data mining. This paper proposes a quantum semi-supervised classifier based on label propagation. Considering the difficulty of graph construction, we develop a variational quantum label propagation (VQLP) method. In this method, a locally parameterized quantum circuit is created to reduce the parameters required in the optimization. Furthermore, we design a quantum semi-supervised binary classifier based on hybrid Bell and $Z$ bases measurement, which has shallower circuit depth and is more suitable for implementation on near-term quantum devices. We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set, and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier. This work opens a new path to quantum machine learning based on graphs.

arXiv:2303.07906Mar 14, 20230 citations

Evolutionary-enhanced quantum supervised learning model

Anton Simen Albino, Rodrigo Bloot, Otto Menegasso Pires +1 more

Quantum supervised learning, utilizing variational circuits, stands out as a promising technology for NISQ devices due to its efficiency in hardware resource utilization during the creation of quantum feature maps and the implementation of hardware-efficient ansatz with trainable parameters. Despite these advantages, the training of quantum models encounters challenges, notably the barren plateau phenomenon, leading to stagnation in learning during optimization iterations. This study proposes an innovative approach: an evolutionary-enhanced ansatz-free supervised learning model. In contrast to parametrized circuits, our model employs circuits with variable topology that evolves through an elitist method, mitigating the barren plateau issue. Additionally, we introduce a novel concept, the superposition of multi-hot encodings, facilitating the treatment of multi-classification problems. Our framework successfully avoids barren plateaus, resulting in enhanced model accuracy. Comparative analysis with variational quantum classifiers from the technology's state-of-the-art reveal a substantial improvement in training efficiency and precision. Furthermore, we conduct tests on a challenging dataset class, traditionally problematic for conventional kernel machines, demonstrating a potential alternative path for achieving quantum advantage in supervised learning for NISQ era.Quantum supervised learning, utilizing variational circuits, stands out as a promising technology for NISQ devices due to its efficiency in hardware resource utilization during the creation of quantum feature maps and the implementation of hardware-efficient ansatz with trainable parameters. Despite these advantages, the training of quantum models encounters challenges, notably the barren plateau phenomenon, leading to stagnation in learning during optimization iterations. This study proposes an innovative approach: an evolutionary-enhanced ansatz-free supervised learning model. In contrast to parametrized circuits, our model employs circuits with variable topology that evolves through an elitist method, mitigating the barren plateau issue. Additionally, we introduce a novel concept, the superposition of multi-hot encodings, facilitating the treatment of multi-classification problems. Our framework successfully avoids barren plateaus, resulting in enhanced model accuracy. Comparative analysis with variational quantum classifiers from the technology's state-of-the-art reveal a substantial improvement in training efficiency and precision. Furthermore, we conduct tests on a challenging dataset class, traditionally problematic for conventional kernel machines, demonstrating a potential alternative path for achieving quantum advantage in supervised learning for NISQ era.

arXiv:2311.08081Nov 14, 20230 citations

Quantum computing methods for supervised learning

Viraj Kulkarni, Milind Kulkarni, Aniruddha Pant

arXiv:2006.12025Quantum Machine IntelligenceSep 6, 202138 citations

Z

bases measurement, which has shallower circuit depth and is more suitable for implementation on near-term quantum devices. We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set, and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier. This work opens a new path to quantum machine learning based on graphs.