# SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecture

arXiv: https://arxiv.org/abs/2211.12711 · HTML: https://mlsanity.com/paper/2211.12711/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 69 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 26 of 26)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Symmetric Pruning in Quantum Neural Networks](https://mlsanity.com/paper/2208.14057/) (2022)
- [Stochastic noise can be helpful for variational quantum algorithms](https://mlsanity.com/paper/2210.06723/) (2022)
- [Revisiting dequantization and quantum advantage in learning tasks](https://mlsanity.com/paper/2112.00811/) (2021)
- [Laziness, Barren Plateau, and Noise in Machine Learning](https://mlsanity.com/paper/2206.09313/) (2022)
- [Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU(d) Symmetry](https://mlsanity.com/paper/2207.07250/) (2022)
- [Quantum Kerr Learning](https://mlsanity.com/paper/2205.12004/) (2022)

## Built on by (most cited first, 7 of 7)

- [Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers](https://mlsanity.com/paper/2311.16082/) (2023)
- [Symmetry-invariant quantum machine learning force fields](https://mlsanity.com/paper/2311.11362/) (2023)
- [On the universality of Sn-equivariant k-body gates](https://mlsanity.com/paper/2303.00728/) (2023)
- [All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks](https://mlsanity.com/paper/2309.07250/) (2023)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting](https://mlsanity.com/paper/2311.16214/) (2023)
- [RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training](https://mlsanity.com/paper/2311.16035/) (2023)

## Abstract (arXiv)

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× better performance on 3 × 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.