The variational quantum eigensolver (VQE) is currently the flagship algorithm
for molecular simulations on near-term quantum computers. The
algorithm involves implementing a sequence of parameterized gates on quantum
hardware to generate a target quantum state and measuring the molecular energy.
The number of gates that can be implemented on current quantum devices remains
limited mainly due to finite coherence times and frequent gate errors,
preventing accurate applications to systems with significant entanglement,
such as strongly correlated molecules.
In this work, we present an alternate approach (which we refer to as ctrl-VQE)
where the quantum circuit used for state preparation is removed entirely and
replaced by a quantum optimal 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 ground state molecular energy. By removing the
quantum circuit, the coherence times required for state preparation can be
drastically reduced by directly optimizing the pulses at the device level. 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. We further present an adaptive pulse
shaping algorithm to avoid overparameterization of pulse parameters.