  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.
