Preparing Hartree-Fock Ansatze with a Polylogarithmic Two-Qubit Gate Depth Circuit on a Quantum Computer

Quantum state preparation is a critical subroutine in quantum computing applications for quantum chemistry. Hartree-Fock (HF) ansatze are popular initial quantum states to prepare as it serves as a fundamental starting point in many quantum chemistry methods. HF ansatze are one-body product wavefunctions that approximate the solution to the Schrödinger equation for many-body systems, such as molecules and materials.

In this work, we shall demonstrate how HF ansatze can be efficiently prepared on a quantum computer. By adapting methods from recent developments in quantum machine learning, we can prepare HF ansatze with a polylogarithmic two-qubit gate depth quantum circuit with respect to the molecule basis set size, offering a subexponential reduction in gate depth scaling over existing linear-depth approaches. In addition, we extended our method to prepare correlated states which have even shallower circuit depth than that of the HF ansatze. Such efficient quantum state preparation methods will potentially enable high-accuracy studies of molecular systems with large basis sets on near-term quantum computers.