[Paper Review] Trainable Discrete Feature Embeddings for Variational Quantum Classifier

Napat Thumwanit, Chayaphol Lortaraprasert+2 more|arXiv (Cornell University)|Jun 17, 2021

Quantum Computing Algorithms and Architecture38 references4 citations

TL;DR

This paper proposes trainable discrete feature embeddings for variational quantum classifiers by combining Quantum Random Access Coding (QRAC) with quantum metric learning, enabling fewer qubits and improved classification of hard Boolean functions like parity. The method achieves higher accuracy than fixed QRAC embeddings and works effectively on real quantum hardware, demonstrating viability for near-term quantum machine learning with discrete data.

ABSTRACT

Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC), an important primitive to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning. We show that the proposed trainable embedding requires not only as few qubits as QRAC but also overcomes the limitations of QRAC to classify inputs whose classes are based on hard Boolean functions. We numerically demonstrate its use in variational quantum classifiers to achieve better performances in classifying real-world datasets, and thus its possibility to leverage near-term quantum computers for quantum machine learning.

Motivation & Objective

• To address the limitation of fixed QRAC-based embeddings in classifying discrete data with hard Boolean functions, such as parity, which are not linearly separable in quantum state space.
• To develop a trainable quantum feature embedding method that maintains the qubit efficiency of QRAC while overcoming its fixed mapping constraints.
• To enable effective training of variational quantum classifiers on real quantum hardware using discrete features with minimal qubit overhead.
• To demonstrate that trainable embeddings can generalize better than fixed QRAC mappings, especially on complex decision boundaries.
• To provide a flexible framework for quantum machine learning applicable to real-world datasets with categorical or discrete features.

Proposed method

• Combines QRAC for qubit-efficient encoding of discrete features with quantum metric learning to train embeddings that optimize state separation in Hilbert space.
• Uses a differentiable quantum circuit to learn optimal parameterized quantum states for each discrete input, enabling end-to-end training.
• Applies regularization (e.g., λ = 0.02) to prevent overfitting and improve generalization during optimization.
• Employs a linearly entangled RyRz circuit on IBM's ibmq_athens to reduce CNOT gate count due to hardware connectivity constraints.
• Leverages a hybrid quantum-classical optimization loop, where classical optimizers update quantum circuit parameters based on gradient information.
• Uses a loss function based on cross-entropy to train the classifier, with training monitored via validation accuracy and loss curves.

Experimental results

Research questions

• RQ1 Can trainable embeddings overcome the linear separability limitations of fixed QRAC mappings when classifying hard Boolean functions like parity?
• RQ2 Can the proposed method achieve high classification accuracy on real-world datasets using fewer qubits than standard QRAC-based approaches?
• RQ3 Is the trainable embedding framework compatible with and effective on near-term noisy intermediate-scale quantum (NISQ) devices?
• RQ4 How does the performance of trainable embeddings compare to fixed QRAC mappings in terms of generalization and convergence on real hardware?
• RQ5 Can the method be generalized to arbitrary (m,n) mappings even when no optimal QRAC exists, such as (4,1)-QRAC?

Key findings

• The trainable embedding achieved 100% test accuracy on the 6-bit parity problem on both simulation and real hardware (ibmq_athens), outperforming fixed QRAC mappings which require additional qubits for such tasks.
• On the Titanic survival dataset, the method achieved 71.5% training and 70.9% test accuracy using only 3 qubits, demonstrating strong performance on real-world data.
• The method maintained high accuracy with minimal qubit overhead, showing that (4,1)-TE is effective despite the non-existence of an optimal (4,1)-QRAC.
• Training on real hardware showed convergence with higher fluctuation than simulation, likely due to noise, but still achieved stable performance with only 100 epochs.
• The convolutional TE variant achieved better performance than other TE types, even with only 9 qubits, though with increased parameter count.
• The results demonstrate that trainable embeddings are viable for real-world quantum machine learning tasks and can be deployed on current NISQ devices.