Data re-uploading for a universal quantum classifier (1907.02085v3)

Abstract: A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.

• The paper shows that single qubits can form complex decision boundaries by repeatedly re-uploading classical data.
• The approach leverages the Universal Approximation Theorem to enable intricate function approximation with minimal quantum resources.
• Layered quantum circuits with repetitive encoding boost classification accuracy, achieving success rates of up to 98%.

Data Re-uploading for a Universal Quantum Classifier

The paper discusses a novel approach to quantum classification using the concept of data re-uploading, which enables a single qubit to function as a universal quantum classifier. This capability is achieved by integrating classical subroutines with quantum operations, effectively compensating for the simplistic nature of single qubits through multiple data re-uploads within the quantum circuit.

Core Contributions

1. Single Qubit Capacity: The authors outline how a single qubit, despite its inherent limitations in computational capacity, can be leveraged to classify data efficiently by repeatedly re-uploading classical data into quantum states. This process allows the quantum circuit to form complex decision boundaries analogous to neural networks.
2. Data Re-uploading and Universal Approximation: The paper draws a parallel between the mechanism of data re-uploading in quantum circuits and the Universal Approximation Theorem, which states that a neural network with a single hidden layer can approximate any continuous function given sufficient width. Here, re-uploading classical data into the quantum system multiple times allows for intricate function approximation using limited quantum resources.
3. Layered Quantum Circuits: Each layer in the proposed quantum circuit involves encoding classical data and parameters followed by quantum processing, which enhances the circuit's representational power. Essentially, a single-qubit rotation gate is used as a basic building block that, when applied sequentially, can develop sophisticated classifiers.
4. Benchmarking and Performance: Through extensive benchmarking on various classification tasks—ranging from simple geometric patterns to more complex multidimensional patterns—the effectiveness of single and multi-qubit classifiers is validated. Notably, improvements in classification accuracy are observed with the addition of qubits and entanglement, signifying enhanced performance capabilities.

Numerical Performance and Metrics

• Accuracy: The classifiers demonstrate a significant success rate across diverse problems, consistently achieving high accuracy in classification tasks, sometimes surpassing classical methods such as neural networks and SVMs. For example, results indicate success rates of up to 98% in classifying non-convex shapes and multidimensional spheres.
• Efficiency with Increasing Complexity: The inclusion of multiple qubits and the introduction of entanglement are shown to reduce the necessary circuit depth significantly while maintaining or improving classification success rates. This feature suggests practical scalability of the approach to more complex datasets.

Implications and Future Directions

The implications of this work are manifold. Practically, the presented method offers a new avenue for implementing quantum classifiers that minimize quantum resource demands, making them particularly suitable for NISQ devices. Theoretically, the research hints at potential frameworks for merging classical computational approaches with quantum mechanics, paving the way for hybrid algorithms that capitalize on both classical and quantum computation's strengths.

Future research could explore optimizing state preparation methods to further reduce computational overhead and improve error resilience. Investigating alternative entangling strategies and parameter optimization techniques could unveil additional performance gains. Furthermore, the exploration of this universal classifier's potential in handling real-world datasets, particularly in fields like medicine or finance, offers exciting prospects for realizing quantum computing's practical benefits.

Ultimately, this paper contributes to the broader understanding of how minimal quantum systems, when combined with innovative strategies like data re-uploading, can significantly enhance computational capabilities in quantum machine learning tasks.