Evaluating Ground State Energy with Low-Depth Quantum Circuit and High Accuracy*

Solving electronic structure problems is widely recognized as one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the NISQ (Noisy Intermediate Scale Quantum) era, it's vital to design algorithms with shallow circuits.

In this project, we develop a novel Variational Quantum Eigensolver (VQE) ansatz based on the QCC (Qubit Coupled Cluster) [1, 2] approach, which demands optimization over only n parameters rather than the usual n+2m parameters, where n represents the number of Pauli word time evolution gates e^-itP, and m is the number of qubits involved.

We evaluate the ground state energy of O₃, Li₄, Cr₂, and C₄H₈, using CASCI(4,4) method in conjunction with the enhanced QCC ansatz, UCCSD (Unitary Coupled Cluster Single-Double) ansatz, or FCI (Full Configuration Interaction) method as the active space solver. Furthermore, we assess our enhanced QCC ansatz on two distinct quantum hardware platforms, one superconducting-based and one trapped-ion-based. In the end, we conclude with a gate count analysis on both setups.

References

(1) Ryabinkin, I. G.; Yen, T.-C.; Genin, S. N.; Izmaylov, A. F. Journal of Chemical Theory and Computation 2018, 14, 6317–6326.

(2) Ryabinkin, I. G.; Lang, R. A.; Genin, S. N.; Izmaylov, A. F. Journal of Chemical Theory and Computation 2020, 16, 1055–1063.