  In this work we investigate methods to improve the efficiency and scalability
of quantum algorithms for quantum chemistry applications. We propose a
transformation of the electronic structure Hamiltonian in the second
quantization framework into the particle-hole (p/h) picture, which offers a
better starting point for the expansion of the trial wavefunction. The state of
the molecular system at study is parametrized in a way to efficiently explore
the sector of the molecular Fock space that contains the desired solution. To
this end, we explore several trial wavefunctions to identify the most efficient
parameterization of the molecular ground state. Taking advantage of known
post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space
search quantum algorithms, we propose a new family of quantum circuits based on
exchange-type gates that enable accurate calculations while keeping the gate
count (i.e., the circuit depth) low. The particle-hole implementation of the
Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver
approach gives rise to an efficient quantum algorithm, named q-UCC , with
important advantages compared to the straightforward 'translation' of the
classical Coupled Cluster counterpart. In particular, we show how a single
Trotter step can accurately and efficiently reproduce the ground state energies
of simple molecular systems.
