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This work tackles the problem of finding a good ansatz initialization forVariational Quantum Algorithms (VQAs), by proposing CAFQA, a Clifford AnsatzFor Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit builtwith only Clifford gates. In this ansatz, the parameters for the tunable gatesare chosen by searching efficiently through the Clifford parameter space viaclassical simulation. The resulting initial states always equal or outperformtraditional classical initialization (e.g., Hartree-Fock), and enablehigh-accuracy VQA estimations. CAFQA is well-suited to classical computationbecause: a) Clifford-only quantum circuits can be exactly simulated classicallyin polynomial time, and b) the discrete Clifford space is searched efficientlyvia Bayesian Optimization.  For the Variational Quantum Eigensolver (VQE) task of molecular ground stateenergy estimation (up to 18 qubits), CAFQA's Clifford Ansatz achieves a meanaccuracy of nearly 99% and recovers as much as 99.99% of the molecularcorrelation energy that is lost in Hartree-Fock initialization. CAFQA achievesmean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, ondifferent metrics. The scalability of the approach allows for preliminaryground state energy estimation of the challenging chromium dimer (Cr$_2$)molecule. With CAFQA's high-accuracy initialization, the convergence of VQAs isshown to accelerate by 2.5x, even for small molecules.  Furthermore, preliminary exploration of allowing a limited number ofnon-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% ofthe correlation energy can be recovered at bond lengths for which Clifford-onlyCAFQA accuracy is relatively limited, while remaining classically simulable.

CAFQA: A classical simulation bootstrap for variational quantum algorithms