Fermionic quantum processing with programmable neutral atom arrays.

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.

Scalable Cold-Atom Quantum Simulator for Two-Dimensional QED.

We propose a scalable analog quantum simulator for quantum electrodynamics in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs interspecies spin-changing collisions in an ultracold atomic mixture trapped in an optical lattice. We engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle toward experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to the pure gauge theory of compact QED and discuss how the phenomenon of confinement of electric charges can be described by the quantum simulator.

Dynamical Topological Transitions in the Massive Schwinger Model with a θ Term.

Aiming at a better understanding of anomalous and topological effects in gauge theories out of equilibrium, we study the real-time dynamics of a prototype model for CP violation, the massive Schwinger model with a θ term. We identify dynamical quantum phase transitions between different topological sectors that appear after sufficiently strong quenches of the θ parameter. Moreover, we establish a general dynamical topological order parameter, which can be accessed through fermion two-point correlators and, importantly, which can be applied for interacting theories. Enabled by this result, we show that the topological transitions persist beyond the weak-coupling regime. Finally, these effects can be observed with tabletop experiments based on existing cold-atom, superconducting-qubit, and trapped-ion technology. Our Letter thus presents a significant step towards quantum simulating topological and anomalous real-time phenomena relevant to nuclear and high-energy physics.