A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

TL;DR

This work tackles the bottleneck of limited qubits and noise in near-term quantum devices by proposing co-TenQu, a quantum-classical hybrid training architecture that combines a trainable tensor network for data compression with a quantum circuit trained via a quantum-state fidelity cost measured through a SWAP test. The classical TN pre-processes and compresses data, enabling a smaller quantum circuit, while the quantum portion is trained directly on quantum states, leading to better utilization of quantum resources. Empirical results show up to a $41.72\%$ improvement over a strong classical baseline and up to $1.9\times$ gains over other quantum methods, with significant qubit-resource savings (up to $70.59\%$ fewer qubits). The work demonstrates the viability of collaborative quantum-classical training for scalable quantum machine learning on current hardware and lays a path for extending fidelity-based objectives to more complex architectures and applications.

Abstract

Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can leverage quantum computers. Moreover, as the available qubits increase, the computational complexity grows exponentially, posing additional challenges. Consequently, there is an urgent need to use qubits efficiently and mitigate both present limitations and future complexities. To address this, existing quantum applications attempt to integrate classical and quantum systems in a hybrid framework. In this study, we concentrate on quantum deep learning and introduce a collaborative classical-quantum architecture called co-TenQu. The classical component employs a tensor network for compression and feature extraction, enabling higher-dimensional data to be encoded onto logical quantum circuits with limited qubits. On the quantum side, we propose a quantum-state-fidelity-based evaluation function to iteratively train the network through a feedback loop between the two sides. co-TenQu has been implemented and evaluated with both simulators and the IBM-Q platform. Compared to state-of-the-art approaches, co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. Additionally, it outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.

Figures (15)

• Figure 1: CNOT Gate Circuit Notation
• Figure 2: Swap Test Quantum Circuit
• Figure 3: co-TenQu: A Quantum-Classical Collaborative Training Architecture
• Figure 4: Single Qubit Unitary
• Figure 5: Dual Qubit