This work tackles the problem of finding a good ansatz initialization for Variational Quantum Algorithms (VQAs), 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 (Cr$_2$) 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.

翻译：本研究针对变分量子算法（VQA）中拟设初始化的难题，提出了CAFQA方法——一种基于克利福德拟设的量子精度提升方案。该拟设采用仅含克利福德门的硬件高效电路结构，通过经典模拟高效搜索克利福德参数空间，选择可调门参数。由此生成的初始状态始终优于或等同于传统经典初始化（如哈特里-福克方法），并可实现高精度VQA估算。CAFQA特别适用于经典计算的原因在于：(a) 仅含克利福德门的量子电路可在多项式时间内通过经典计算精确模拟；(b) 离散克利福德空间可通过贝叶斯优化实现高效搜索。在分子基态能量估计（最多18量子比特）的变分量子本征求解器（VQE）任务中，CAFQA的克利福德拟设平均精度接近99%，可恢复哈特里-福克初始化丢失的多达99.99%的分子关联能。在不同评估指标上，CAFQA的平均精度较当前最优方法分别提升6.4倍和56.8倍。该方法具备良好可扩展性，可对具有挑战性的铬二聚体（Cr₂）分子进行初步基态能量估计。即使对于小分子，采用CAFQA高精度初始化后，VQA的收敛速度仍可提升2.5倍。此外，初步探索表明，在CAFQA框架中允许有限数量的非克利福德（T）门，可在纯克利福德CAFQA精度受限的键长区域恢复高达99.9%的关联能，同时保持经典可模拟性。