  Variational quantum eigensolvers offer a small-scale testbed to demonstrate
the performance of error mitigation techniques with low experimental overhead.
We present successful error mitigation by applying the recently proposed
symmetry verification technique to the experimental estimation of the
ground-state energy and ground state of the hydrogen molecule. A finely
adjustable exchange interaction between two qubits in a circuit QED processor
efficiently prepares variational ansatz states in the single-excitation
subspace respecting the parity symmetry of the qubit-mapped Hamiltonian.
Symmetry verification improves the energy and state estimates by mitigating the
effects of qubit relaxation and residual qubit excitation, which violate the
symmetry. A full-density-matrix simulation matching the experiment dissects the
contribution of these mechanisms from other calibrated error sources. Enforcing
positivity of the measured density matrix via scalable convex optimization
correlates the energy and state estimate improvements when using symmetry
verification, with interesting implications for determining system properties
beyond the ground-state energy.
