Young Min Rhee

The electron pair approximation offers a resource efficient variational quantum eigensolver (VQE) approach for quantum chemistry simulations on quantum computers. With the number of entangling gates scaling quadratically with system size and a constant energy measurement overhead, the orbital optimized unitary pair coupled cluster double (oo-upCCD) ansatz strikes a balance between accuracy and efficiency on today's quantum computers. However, the electron pair approximation makes the method incapable of producing quantitatively accurate energy predictions. In order to improve the accuracy without increasing the circuit depth, we explore the idea of reduced density matrix (RDM) based second order perturbation theory (PT2) as an energetic correction to electron pair approximation. The new approach takes into account of the broken-pair energy contribution that is missing in pair-correlated electron simulations, while maintaining the computational advantages of oo-upCCD ansatz. In dissociations of N$_2$, Li$_2$O, and chemical reactions such as the unimolecular decomposition of CH$_2$OH$^+$ and the \snTwo reaction of CH$_3$I $+$ Br$^-$, the method significantly improves the accuracy of energy prediction. On two generations of the IonQ's trapped ion quantum computers, Aria and Forte, we find that unlike the VQE energy, the PT2 energy correction is highly noise-resilient. By applying a simple error mitigation approach based on post-selection solely on the VQE energies, the predicted VQE-PT2 energy differences between reactants, transition state, and products are in excellent agreement with noise-free simulators.

Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ's Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters - the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.