Linear Depth Circuit Unitary Coupled Cluster Wavefunctions for Quantum Computation

Motivated by the rapid development of quantum computing hardware we introduce a new unitary coupled cluster wavefunction ansatz for quantum chemistry which we call k-UpCCGSD. k-UpCCGSD employs k products of the exponential of a sparse generalized doubles excitation operator, together with generalized single excitation operators, resulting in a wavefunction which can be approximated by a linear-depth circuit. We compare its performance with that of the generalized unitary coupled cluster ansatz employing the full generalized singles and doubles excitation operators (UCCGSD), as well as with the standard ansatz containing only excitations between occupied and virtual orbitals (UCCSD). We find that k-UpCCGSD offers an appealing tradeoff between accuracy and cost, and dramatically outperforms the standard UCCSD, particularly for the calculation of low-lying excited states.