[Paper Review] SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecture

Han Zheng, Christopher Kang+5 more|arXiv (Cornell University)|Nov 23, 2022

Quantum Computing Algorithms and Architecture64 references4 citations

TL;DR

This paper proposes SnCQA, a hardware-efficient variational quantum circuit architecture that respects $S_n$ permutation and spatial lattice symmetries, enabling scalable, accurate, and noise-resilient quantum machine learning. It achieves 20× better performance and 200–1000% resource savings compared to pure hardware-efficient ansatz (pHEA) in learning ground states of 2D Heisenberg models.

ABSTRACT

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 $20 imes$ better performance on $3 imes 4$ 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.

Motivation & Objective

• To design a variational quantum circuit architecture that respects permutation and spatial lattice symmetries for improved efficiency in quantum machine learning.
• To enable hardware-efficient implementation of symmetry-respecting quantum circuits suitable for near-term NISQ devices.
• To benchmark performance against traditional pHEA ansatz in terms of convergence speed, parameter count, and noise resilience.
• To investigate whether symmetry-aware design reduces barren platetform risk and enhances robustness to quantum noise.
• To demonstrate scalability and practical viability in quantum computational chemistry problems, particularly ground state energy estimation.

Proposed method

• Constructs a quantum circuit architecture based on the QAOA framework with $S_n$ permutation symmetry and lattice automorphism symmetry.
• Implements hardware-efficient versions using parametrized single- and two-qubit gates, minimizing circuit depth and gate count.
• Employs symmetry-preserving ansatz initialization via quantum Schur transform to reduce effective Hilbert space dimension.
• Uses adjacent eSWAPs and second-order Hamiltonians to ensure universality within charge sectors, supporting expressibility.
• Applies noise simulation to evaluate resilience under measurement and depolarizing noise, comparing performance to pHEA.
• Optimizes variational parameters using gradient-based methods on frustration-free antiferromagnetic Heisenberg models on 2D square lattices.

Experimental results

Research questions

• RQ1 Can a symmetry-respecting quantum circuit architecture achieve better convergence and lower resource usage than standard pHEA in quantum machine learning tasks?
• RQ2 How does incorporating $S_n$ permutation and spatial lattice symmetries affect the scalability and noise resilience of variational quantum circuits?
• RQ3 To what extent does symmetry-aware design mitigate the barren plateau problem in variational quantum algorithms?
• RQ4 Can hardware-efficient implementations of symmetric ansätze be practically realized on near-term quantum devices with limited qubit coherence?
• RQ5 Does the use of symmetry lead to improved performance in learning ground states of quantum many-body systems like the Heisenberg model?

Key findings

• SnCQA achieves 20× better performance than pHEA in convergence speed and accuracy when learning ground states of 2D Heisenberg models.
• Resource usage is reduced by 200–1000% across various lattice sizes, with fewer layers, parameters, and faster convergence times.
• The circuit demonstrates strong noise resilience, maintaining high performance under measurement and depolarizing noise, suggesting practical viability on NISQ devices.
• Symmetry-preserving initialization and reduced effective dimension suppress barren plateaus, enhancing training stability.
• The architecture is scalable and universal within charge sectors, with theoretical and numerical evidence supporting its expressibility.
• Decoherence-free subspaces and symmetry-induced saddle-point avoidance may contribute to enhanced robustness, aligning with observed noise resilience.