  Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm
designed for noisy intermediate-scale quantum (NISQ) computers. It is promising
for quantum chemical calculations (QCC) because it can calculate the
ground-state energy of a target molecule. Although VQE has a potential to
achieve a higher accuracy than classical approximation methods in QCC, it is
challenging to achieve it on current NISQ computers due to the significant
impact of noises. Density matrix embedding theory (DMET) is a well-known
technique to divide a molecule into multiple fragments, which is available to
mitigate the noise impact on VQE. However, our preliminary evaluation shows
that the naive combination of DMET and VQE does not outperform a gold standard
classical method.
  In this work, we present three approaches to mitigate the noise impact for
the DMET+VQE combination. (1) The size of quantum circuits used by VQE is
decreased by reducing the number of bath orbitals which represent interactions
between multiple fragments in DMET. (2) Reduced density matrices (RDMs), which
are used to calculate a molecular energy in DMET, are calculated accurately
based on expectation values obtained by executing quantum circuits using a
noise-less quantum computer simulator. (3) The parameters of a quantum circuit
optimized by VQE are refined with mathematical post-processing. The evaluation
using a noisy quantum computer simulator shows that our approaches
significantly improve the accuracy of the DMET+VQE combination. Moreover, we
demonstrate that on a real NISQ device, the DMET+VQE combination applying our
three approaches achieves a higher accuracy than the gold standard classical
method.
