Symmetric Pruning in Quantum Neural Networks
This work addresses the challenge of improving QNN efficiency for quantum computing applications, offering a theoretical explanation and practical method, though it is incremental as it builds on existing over-parameterization theory.
The paper tackles the problem of enhancing quantum neural networks (QNNs) for ground state preparation by proposing the effective quantum neural tangent kernel (EQNTK) to explain why symmetric ansatzes improve trainability, and introduces a symmetric pruning scheme that automatically tailors symmetric ansatzes to boost performance, with numerical simulations validating the approach.
Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern quantum machines, have emerged as a leading protocol to conquer this issue. As such, how to enhance the performance of QNNs becomes a crucial topic in GSP. Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes, while theoretical explanations have not been explored. To fill this knowledge gap, here we propose the effective quantum neural tangent kernel (EQNTK) and connect this concept with over-parameterization theory to quantify the convergence of QNNs towards the global optima. We uncover that the advance of symmetric ansatzes attributes to their large EQNTK value with low effective dimension, which requests few parameters and quantum circuit depth to reach the over-parameterization regime permitting a benign loss landscape and fast convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme to automatically tailor a symmetric ansatz from an over-parameterized and asymmetric one to greatly improve the performance of QNNs when the explicit symmetry information of Hamiltonian is unavailable. Extensive numerical simulations are conducted to validate the analytical results of EQNTK and the effectiveness of SP.