Hierarchical quantum classifiers (1804.03680v2)

Abstract: Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer.

• The paper demonstrates that hierarchical quantum circuits leveraging TTN and MERA structures achieve enhanced binary classification for both classical and quantum data.
• It introduces ancilla-augmented three-qubit gates that yield up to 64.05% accuracy on synthetic quantum datasets, marking a pivotal advancement in quantum data handling.
• Experimental tests on IBM's quantum hardware reveal that TTN-based classifiers maintain high resilience to noise while achieving 100% accuracy on benchmark datasets.

Hierarchical Quantum Classifiers: Advancing Quantum Machine Learning

The paper "Hierarchical Quantum Classifiers" focuses on leveraging quantum circuits with hierarchical structures for enhancing binary classification tasks in machine learning, with a particular emphasis on classifying both classical data and highly entangled quantum states. Such configurations primarily utilize Tree Tensor Networks (TTN) and Multi-Scale Entanglement Renormalization Ansatz (MERA) within quantum computing frameworks. By adopting quantum circuits that require fewer parameters to match expressiveness levels, as compared to some traditional machine learning models, this research elucidates on the computational efficiency and classification efficacy achievable through hierarchical quantum structures.

Key Findings and Numerical Results

1. Circuit Expressiveness and Robustness: It was demonstrated that circuits with greater expressiveness, especially those conforming to MERA structures, achieve superior classification accuracy over simpler TTNs. This improvement was consistent across various datasets including popular classical machine learning benchmarks such as the Iris and MNIST datasets, and synthetic quantum datasets.
2. Handling Quantum Data: A notable achievement of this work is the ability to classify quantum states efficiently—a task for which there is no known classical equivalent. In particular, ancilla-augmented three-qubit gates were found necessary for achieving this, demonstrating classification accuracies of up to 64.05% for certain synthetic quantum datasets.
3. Experimental Validation on Quantum Hardware: Testing the algorithms on the IBM Quantum Experience’s ibmqx4 quantum computer, the research illustrated that the proposed quantum classifiers maintain high accuracies even under realistic noise conditions. Experiments displayed resilience to depolarizing noise up to a threshold, with the TTN-based Iris dataset classifier achieving a test accuracy of 100% in quantum deployment scenarios.

Implications and Theoretical Impacts

The research presented opens several avenues both in theoretical explorations and practical applications:

• Scalability: The circuits, by virtue of their hierarchical nature, inherently support scalability to larger quantum data inputs, which is crucial for practical implementations on burgeoning quantum computing platforms.
• Regularization Benefits: The strict unitary constraints imposed on quantum circuits naturally serve as a form of regularization, potentially aiding in mitigating overfitting—a common challenge in machine learning tasks.
• Potential for Hybrid Quantum-Classical Models: The reported synergy in hybrid models, where classical pre-training of TTN classifiers helps enhance the initialization of MERA circuits, suggests a viable approach for future model developments on near-term quantum hardware.

Future Directions

The findings prompt numerous questions ripe for further inquiry:

• Architectural Optimization: Identifying the optimal quantum circuit architecture for specific machine learning tasks remains a substantial challenge that may hold key insights for improving classifier models.
• Extended Data Encoding: Exploring qudit-based models rather than qubits might offer richer architectures that handle larger input spaces more effectively.
• Role of Entanglement: Further dissecting the complex interplay between quantum entanglement and classification accuracy, especially in higher dimensional circuit layouts, might pave the way for new optimization techniques in quantum machine learning.

Concluding, the research systematically builds upon both theoretical and practical frameworks to substantiate the role of hierarchical quantum classifiers in contemporary machine learning. It sets a foundational precedent in utilizing advanced quantum state manipulations for real-world data classification, heralding a promising step towards robust quantum machine learning solutions.