Fermionic quantum processing with programmable neutral atom arrays - González-Cuadra, D.; Bluvstein, D.; Kalinowski, M.; Kaubruegger, R.; Maskara, N.; Naldesi, P.; Zache, T. V.; Kaufman, A. M.; Lukin, M. D.; Pichler, H.; Vermersch, B.; Ye, Jun; et al. (Proceedings of the National Academy of Sciences - PNAS, 2023)
SignificanceNeutral atoms trapped in tweezer arrays have recently emerged as powerful quantum simulation platforms, with recent experiments targeting quantum spin models. In this work, we envision the next generation of programmable atomic quantum simulators, where not only the atom’s internal but also motional degrees of freedom are controlled to process quantum information. In the case of fermionic atoms, this allows to encode and simulate fermionic models locally, where Fermi statistics are guaranteed at the hardware level. We develop a set of fermionic quantum gates acting on this fermionic register, including digital tunneling gates, and use it to construct fermionic circuits. This approach reduces circuit depths for quantum simulation significantly compared to qubit encodings, which always incur resource overheads. Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.