Enabling Non-Linear Quantum Operations through Variational Quantum Splines
This work addresses the problem of enabling non-linear operations in quantum machine learning for researchers and practitioners, offering a more practical and hardware-efficient solution compared to prior methods, though it is incremental as it builds on existing Quantum Splines.
The authors tackled the limitation of linear operations in quantum machine learning by proposing Generalised Hybrid Quantum Splines (GHQSplines), a method for approximating non-linear quantum activation functions using hybrid quantum-classical computation, which outperforms the original Quantum Splines in fitting quality and can be implemented on near-term quantum computers.
The postulates of quantum mechanics impose only unitary transformations on quantum states, which is a severe limitation for quantum machine learning algorithms. Quantum Splines (QSplines) have recently been proposed to approximate quantum activation functions to introduce non-linearity in quantum algorithms. However, QSplines make use of the HHL as a subroutine and require a fault-tolerant quantum computer to be correctly implemented. This work proposes the Generalised Hybrid Quantum Splines (GHQSplines), a novel method for approximating non-linear quantum activation functions using hybrid quantum-classical computation. The GHQSplines overcome the highly demanding requirements of the original QSplines in terms of quantum hardware and can be implemented using near-term quantum computers. Furthermore, the proposed method relies on a flexible problem representation for non-linear approximation and it is suitable to be embedded in existing quantum neural network architectures. In addition, we provide a practical implementation of the GHQSplines using Pennylane and show that our model outperforms the original QSplines in terms of quality of fitting.