  We formulate and implement the Variational Quantum Eigensolver Self
Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding
(PE), thereby extending PE to the regime of quantum computing. We test the
resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the
computational stress on the quantum device is only slightly increased in terms
of gate counts compared to regular VQE-SCF. On the other hand, no increase in
shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling
of real chemical systems using a simulation of the reaction barrier of the
Diels-Alder reaction between furan and ethene as an example.
