  Application of current and near-term quantum hardware to the electronic
structure problem is highly limited by qubit counts, coherence times, and gate
fidelities. To address these restrictions within the variational quantum
eigensolver (VQE) framework, many recent contributions have suggested dressing
the electronic Hamiltonian to include a part of electron correlation, leaving
the rest to be accounted by VQE state preparation. We present a new dressing
scheme that combines preservation of the Hamiltonian hermiticity and an exact
quadratic truncation of the Baker-Campbell-Hausdorff expansion. The new
transformation is constructed as the exponent of an involutory linear
combination (ILC) of anti-commuting Pauli products. It incorporates important
strong correlation effects in the dressed Hamiltonian and can be viewed as a
classical preprocessing step alleviating the resource requirements of the
subsequent VQE application. The assessment of the new computational scheme for
electronic structure of the LiH, H$_2$O, and N$_2$ molecules shows significant
increase in efficiency compared to conventional qubit coupled cluster
dressings.

Quantum Physics;Chemical Physics