Shallow Quantum Circuits for Deep Chemistry via Valence Bond Embeddings

Quantum chemistry is one of the major potential applications in quantum computation. Currently there is a considerable focus on relatively small active spaces as a consequence of hardware noise and exponential bottlenecks in simulations. In the long run, there will be an increasing demand in reliable approximations for larger systems - both, as initial states for projective algorithms like the quantum phase estimation or for the evaluation of dynamical properties. While numerous approaches to select active spaces and extrapolate basis set accuracy exist, there is currently no consistent approach that results in a single quantum circuit for the total system. In this work, we combine hybrid Fermionic-Bosonic encodings with the structured approach of Quantum Valence Bond Theory to directly construct quantum circuits for comparably large molecular systems. With this approach we are able to push simulability barrier of variational quantum eigensolvers towards chemically relevant systems and demonstrate circuit designs that outperform active space counterparts and achieve good approximations with respect to the exact solutions.