Improved Strategies for Fermionic Quantum Simulation with Global Interactions

Abstract: We present efficient quantum circuits for fermionic excitation operators tailored for ion trap quantum computers exhibiting the M{\o}lmer-S{\o}rensen (MS) gate. Such operators commonly arise in the study of static and dynamic properties in electronic structure problems using Unitary Coupled Cluster theory or Trotterized time evolution. We detail how the global MS interaction naturally suits the non-local structure of fermionic excitation operators under the Jordan-Wigner mapping and simultaneously provides optimal parallelism in their circuit decompositions. Compared to previous schemes on ion traps, our approach reduces the number of MS gates by factors of 2-, and 4, for single-, and double excitations, respectively. This improvement promises significant speedups and error reductions.