  NISQ era devices suffer from a number of challenges like limited qubit
connectivity, short coherence times and sizable gate error rates. Thus, quantum
algorithms are desired that require shallow circuit depths and low qubit counts
to take advantage of these devices. We attempt to realize this with the help of
classical quantum chemical theories of canonical transformation and explicit
correlation. In this work, compact ab initio Hamiltonians are generated
classically through an approximate similarity transformation of the Hamiltonian
with a) an explicitly correlated two-body unitary operator with generalized
pair excitations that remove the Coulombic electron-electron singularities from
the Hamiltonian and b) a unitary one-body operator to efficiently capture the
orbital relaxation effects required for accurate description of the excited
states. The resulting transcorelated Hamiltonians are able to describe both
ground and excited states of molecular systems in a balanced manner. Using the
fermionic-ADAPT-VQE method based on the unitary coupled cluster with singles
and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we
demonstrate that the transcorrelated Hamiltonians can produce ground state
energies comparable to the much larger cc-pVTZ basis. This leads to a potential
reduction in the number of required CNOT gates by more than three orders of
magnitude for the chemical species studied in this work. Furthermore, using the
qEOM formalism in conjunction with the transcorrelated Hamiltonian, we reduce
the errors in excitation energies by an order of magnitude. The transcorrelated
Hamiltonians developed here are Hermitian and contain only one- and two-body
interaction terms and thus can be easily combined with any quantum algorithm
for accurate electronic structure simulations.
