一句话：提出仅含 Clifford 门的 CAFQA ansatz，用经典模拟搜索初始参数，显著提升 VQA 精度与收敛。
在 NISQ 时代，变分量子算法（VQA）依赖参数化酉电路的迭代优化，但量子设备噪声大、资源昂贵，因此需要经典地选取尽可能接近最优的初始参数。本文提出 CAFQA，一种仅由 Clifford 门构成的硬件高效 ansatz，通过经典模拟在离散 Clifford 参数空间中用贝叶斯优化搜索可调门参数。由于 Clifford-only 电路可在多项式时间内被精确经典模拟，该初始化方法高效可行。在分子基态能量估计的 VQE 任务上（最多 18 个量子比特），CAFQA 平均精度接近 99%，最多恢复 Hartree-Fock 初始化所丢失关联能的 99.99%，较当前最优方法在不同指标上平均提升 6.4 倍与 56.8 倍，并使 VQA 收敛加速 2.5 倍；初步还扩展到 Cr2 分子。允许少量非 Clifford 的 T 门时，仍保持经典可模拟性，并可恢复高达 99.9% 的关联能。
Classical computing plays a critical role in the advancement of quantum frontiers in the NISQ era. In this spirit, this work uses classical simulation to bootstrap Variational Quantum Algorithms (VQAs). VQAs rely upon the iterative optimization of a parameterized unitary circuit (ansatz) with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to classically choose the VQA ansatz initial parameters to be as close to optimal as possible to improve VQA accuracy and accelerate their convergence on today’s devices. This work tackles the problem of finding a good ansatz initialization, by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA’s Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2) molecule. With CAFQA’s high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.
@inproceedings{RaviG0KSBLHBC23,
title = {CAFQA: A Classical Simulation Bootstrap for Variational Quantum Algorithms},
author = {Gokul Subramanian Ravi and Pranav Gokhale and Yi Ding and William Kirby and Kaitlin Smith and Jonathan M. Baker and Peter J. Love and Henry Hoffmann and Kenneth R. Brown and Frederic T. Chong},
booktitle = {ASPLOS},
year = {2022},
doi = {10.1145/3567955.3567958}
}