ctrl-VQE: Fast variational quantum eigensolver with gate-free state preparation

The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state. Due to finite coherence times and frequent gate errors, the number of gates that can be implemented remains limited on current quantum devices, preventing accurate applications to systems with significant entanglement, such as strongly correlated molecules. In this work, we propose an alternative algorithm where the quantum circuit used for state preparation is removed entirely and replaced by a quantum control routine which variationally shapes a pulse to drive the initial Hartree-Fock state to the full CI target state. The objective function optimized is the expectation value of the qubit-mapped molecular Hamiltonian. However, by removing the quantum circuit, the coherence times required for state preparation can be drastically reduced by directly optimizing the pulses. We demonstrate the potential of this method numerically by directly optimizing pulse shapes which accurately model the dissociation curves of H₂ and HeH⁺, and the ground state energy for LiH.