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The variational quantum eigensolver (VQE) is currently the flagship algorithmfor solving electronic structure problems on near-term quantum computers. Thishybrid quantum/classical algorithm involves implementing a sequence ofparameterized gates on quantum hardware to generate a target quantum state, andthen measuring the expectation value of the molecular Hamiltonian. Due tofinite coherence times and frequent gate errors, the number of gates that canbe implemented remains limited on current quantum devices, preventing accurateapplications to systems with significant entanglement, such as stronglycorrelated molecules. In this work, we propose an alternative algorithm (whichwe refer to as ctrl-VQE) where the quantum circuit used for state preparationis removed entirely and replaced by a quantum control routine whichvariationally shapes a pulse to drive the initial Hartree-Fock state to thefull CI target state. As with VQE, the objective function optimized is theexpectation value of the qubit-mapped molecular Hamiltonian. However, byremoving the quantum circuit, the coherence times required for statepreparation can be drastically reduced by directly optimizing the pulses. Wedemonstrate the potential of this method numerically by directly optimizingpulse shapes which accurately model the dissociation curves of the hydrogenmolecule (covalent bond) and helium hydride ion (ionic bond), and we computethe single point energy for LiH with four transmons.

Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-VQE