Optimized simulations of fermionic systems on a quantum computer

Abstract

Quantum computing holds promise for simulating microscopic phenomena, offering profound implications across disciplines such as chemistry, condensed matter physics, and high-energy physics, particularly in the accurate simulation of fermions. However, practical implementation requires the optimization of quantum programs to mitigate quantum noise and decoherence effects. Given the constraints of near-term quantum computers, the Variational Quantum Eigensolver (VQE) emerges as a key approach for estimating molecular ground state energies, crucial for determining chemical properties. This work aims to present advancements in optimizing VQE simulations to minimize quantum computational resources. Specifically, this work explores various optimization strategies, including the utilization of second-order perturbation correction to recover additional energy beyond VQE estimates and select critical ansatz terms. Additionally, circuit optimization techniques are investigated, focusing on achieving shorter equivalent ansatz circuits, particularly for physically-inspired VQE ansatz, through methods such as generalized fermion-to-qubit transformations and Pauli string orderings. Furthermore, this work demonstrates the advantage of a better initial state on a trapped-ion quantum computer.