  The variational quantum eigensolver is one of the most promising approaches
for performing chemistry simulations using noisy intermediate-scale quantum
(NISQ) processors. The efficiency of this algorithm depends crucially on the
ability to prepare multi-qubit trial states on the quantum processor that
either include, or at least closely approximate, the actual energy eigenstates
of the problem being simulated while avoiding states that have little overlap
with them. Symmetries play a central role in determining the best trial states.
Here, we present efficient state preparation circuits that respect particle
number, total spin, spin projection, and time-reversal symmetries. These
circuits contain the minimal number of variational parameters needed to fully
span the appropriate symmetry subspace dictated by the chemistry problem while
avoiding all irrelevant sectors of Hilbert space. We show how to construct
these circuits for arbitrary numbers of orbitals, electrons, and spin quantum
numbers, and we provide explicit decompositions and gate counts in terms of
standard gate sets in each case. We test our circuits in quantum simulations of
the $H_2$ and $LiH$ molecules and find that they outperform standard state
preparation methods in terms of both accuracy and circuit depth.
