Resource-efficient equivariant quantum convolutional neural networks

Equivariant quantum neural networks (QNNs) are promising quantum machine learning models that exploit symmetries to provide potential quantum advantages. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum devices remains challenging due to limited computational resources. This study proposes a resource-efficient model of equivariant quantum convolutional neural networks (QCNNs) called equivariant split-parallelizing QCNN (sp-QCNN). Using a group-theoretical approach, we encode general symmetries into our model beyond the translational symmetry addressed by previous sp-QCNNs. We achieve this by splitting the circuit at the pooling layer while preserving symmetry. This splitting structure effectively parallelizes QCNNs to improve measurement efficiency in estimating the expectation value of an observable and its gradient by order of the number of qubits. Our model also exhibits high trainability and generalization performance, including the absence of barren plateaus. Numerical experiments demonstrate that the equivariant sp-QCNN can be trained and generalized with fewer measurement resources than a conventional equivariant QCNN in a noisy quantum data classification task. Our results contribute to the advancement of practical quantum machine learning algorithms.

Quantum Curriculum Learning

Quantum machine learning (QML) requires significant quantum resources to achieve quantum advantage. Research should prioritize both the efficient design of quantum architectures and the development of learning strategies to optimize resource usage. We propose a framework called quantum curriculum learning (Q-CurL) for quantum data, where the curriculum introduces simpler tasks or data to the learning model before progressing to more challenging ones. We define the curriculum criteria based on the data density ratio between tasks to determine the curriculum order. We also implement a dynamic learning schedule to emphasize the significance of quantum data in optimizing the loss function. Empirical evidence shows that Q-CurL enhances the training convergence and the generalization for unitary learning tasks and improves the robustness of quantum phase recognition tasks. Our framework provides a general learning strategy, bringing QML closer to realizing practical advantages.

Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks

Quantum neural networks (QNNs) require an efficient training algorithm to achieve practical quantum advantages. A promising approach is the use of gradient-based optimization algorithms, where gradients are estimated through quantum measurements. However, it is generally difficult to efficiently measure gradients in QNNs because the quantum state collapses upon measurement. In this work, we prove a general trade-off between gradient measurement efficiency and expressivity in a wide class of deep QNNs, elucidating the theoretical limits and possibilities of efficient gradient estimation. This trade-off implies that a more expressive QNN requires a higher measurement cost in gradient estimation, whereas we can increase gradient measurement efficiency by reducing the QNN expressivity to suit a given task. We further propose a general QNN ansatz called the stabilizer-logical product ansatz (SLPA), which can reach the upper limit of the trade-off inequality by leveraging the symmetric structure of the quantum circuit. In learning an unknown symmetric function, the SLPA drastically reduces the quantum resources required for training while maintaining accuracy and trainability compared to a well-designed symmetric circuit based on the parameter-shift method. Our results not only reveal a theoretical understanding of efficient training in QNNs but also provide a standard and broadly applicable efficient QNN design.