  Quantum simulations of electronic structure with a transformed Hamiltonian
that includes some electron correlation effects are demonstrated. The
transcorrelated Hamiltonian used in this work is efficiently constructed
classically, at polynomial cost, by an approximate similarity transformation
with an explicitly correlated two-body unitary operator. This Hamiltonian is
Hermitian, includes no more than two-particle interactions, and is free of
electron-electron singularities. We investigate the effect of such a
transformed Hamiltonian on the accuracy and computational cost of quantum
simulations by focusing on a widely used solver for the Schrodinger equation,
namely the variational quantum eigensolver method, based on the unitary coupled
cluster with singles and doubles (q-UCCSD) Ansatz. Nevertheless, the formalism
presented here translates straightforwardly to other quantum algorithms for
chemistry. Our results demonstrate that a transcorrelated Hamiltonian, paired
with extremely compact bases, produces explicitly correlated energies
comparable to those from much larger bases. For the chemical species studied
here, explicitly correlated energies based on an underlying 6-31G basis had
cc-pVTZ quality. The use of the very compact transcorrelated Hamiltonian
reduces the number of CNOT gates required to achieve cc-pVTZ quality by up to
two orders of magnitude, and the number of qubits by a factor of three.
