Quantum chemistry with subspace states: the conclusion

 Just over a year ago I wrote about a paper on quantum machine learning using subspace states, which inspired a project we undertook on applications of similar quantum states to variational quantum circuits for quantum chemistry and condensed matter physics. Over the weekend our manuscript was published in Physical Review A!

We were fortunate to have three knowledgeable referees who gave constructive and insightful comments on the original manuscript. We heavily revised the manuscript compared to the original arXiv preprint to not only improve the presentation, but also emphasize the broader applicability of the subspace space approach, specifically the ability to prepare correlated fermionic ansatz states beyond pairwise correlations. Our approach can yield substantially shallower quantum circuits for solving problems where the electron density (number of electrons d / number of orbitals used N) is small, for example when trying to extrapolate finite basis set calculations to the complete basis set limit. This is illustrated in the figure below, taken from the paper:

Estimated two-qubit gate depth per occupied mode d to prepare an N-mode Slater determinant and pairwise-correlated ansatz states using subspace states, compared to existing d-independent and linear in N approaches.