Incremental Data-Uploading for Full-Quantum Classification

TL;DR

This work proposes ‘incremental data-uploading’, a novel encoding pattern for high dimensional data that tackles challenges of complex encoding schemes with entanglement and data re- uploading and results in a better representation of data in the quantum circuit with a minimal pre-processing requirement.

Abstract

The data representation in a machine-learning model strongly influences its performance. This becomes even more important for quantum machine learning models implemented on noisy intermediate scale quantum (NISQ) devices. Encoding high dimensional data into a quantum circuit for a NISQ device without any loss of information is not trivial and brings a lot of challenges. While simple encoding schemes (like single qubit rotational gates to encode high dimensional data) often lead to information loss within the circuit, complex encoding schemes with entanglement and data re-uploading lead to an increase in the encoding gate count. This is not well-suited for NISQ devices. This work proposes 'incremental data-uploading', a novel encoding pattern for high dimensional data that tackles these challenges. We spread the encoding gates for the feature vector of a given data point throughout the quantum circuit with parameterized gates in between them. This encoding pattern results in a better representation of data in the quantum circuit with a minimal pre-processing requirement. We show the efficiency of our encoding pattern on a classification task using the MNIST and Fashion-MNIST datasets, and compare different encoding methods via classification accuracy and the effective dimension of the model.

Figures (8)

• Figure 1: Proposed method: The image is downscaled to $10\times 10$, then fed row by row to the 10 bit quantum circuit, each encoding layer (green) is followed by a variational layer (gray), then the 10 qubits are measured (blue).
• Figure 2: Different splits of interleaved layers. For the 1-split, there are 10 encoding layers followed by 10 variational layers, for the 2-split, there are 5 encoding layers, followed by 1 variational layer, then 5 encoding layers, followed by the remaining 9 variational layers. The proposed 10-split is interleaving encoding and variational layers.
• Figure 3: Single encoding block followed by a variational layer. The encoding block and the variational block are repeated 10 times with different intervals in between to form different architectures.
• Figure 4: Average validation accuracy and its standard deviation over 5 training runs for quantum circuits with different splits in the encoding layer. DRU stands for the Data Re-uploading method, and the numbers 1, 2, 4, 8, 10 represents the quantum circuits with 1 whole encoding layer, encoding layer split into 2, 4, 8, 10 blocks respectively.
• Figure 5: Variational layer with 60 parameters used in deeper models.