We propose SnCQA, a set of hardware-efficient variational circuits of
equivariant quantum convolutional circuits respective to permutation symmetries
and spatial lattice symmetries with the number of qubits $n$. By exploiting
permutation symmetries of the system, such as lattice Hamiltonians common to
many quantum many-body and quantum chemistry problems, Our quantum neural
networks are suitable for solving machine learning problems where permutation
symmetries are present, which could lead to significant savings of
computational costs. Aside from its theoretical novelty, we find our
simulations perform well in practical instances of learning ground states in
quantum computational chemistry, where we could achieve comparable performances
to traditional methods with few tens of parameters. Compared to other
traditional variational quantum circuits, such as the pure hardware-efficient
ansatz (pHEA), we show that SnCQA is more scalable, accurate, and noise
resilient (with $20\times$ better performance on $3 \times 4$ square lattice
and $200\% - 1000\%$ resource savings in various lattice sizes and key
criterions such as the number of layers, parameters, and times to converge in
our cases), suggesting a potentially favorable experiment on near-time quantum
devices.

提出了 SnCQA 硬件高效的等变量子卷积电路，适用于存在置换对称性的机器学习问题和量子计算化学中，具有可扩展性和噪声鲁棒性，比传统量子变分电路拥有更高的性能表现。