Quantum Simulation of a Z₂-Lattice Gauge Theory using a Hybrid Spin-Oscillator System

Hybrid spin-oscillator systems offer an efficient encoding for quantum simulations of complex physics problems such as quantum field theories, significantly reducing computational register size and enabling near-term applicability.

Here, we present a quantum simulation of a Z₂ gauge theory coupled to bosonic matter using a trapped-ion hybrid quantum system. Z₂ gauge theories are crucial in understanding phenomena across condensed matter and high-energy physics, such as topological order and confinement. Following our theoretical proposal [1], we encode matter fields in the ion’s harmonic motion and gauge fields in the ion’s electronic states, utilizing the hybrid structure.

To realize the Z₂ Hamiltonian, we extend our technique to create spin-conditioned nonlinear oscillator interaction [2,3] to two oscillator modes. We experimentally demonstrate real-time evolution of a matter excitation on a single gauge-matter link, observing local gauge symmetry. Furthermore, we measure dynamics of entangled gauge fields on an elementary two-dimensional Z₂ plaquette, revealing constructive and destructive tunneling interference due to the Aharonov-Bohm effect.

Finally, we discuss future directions, such as simulating true bosonic matter fields, and outline strategies to scale to larger lattices.

[1] Commun Phys 7, 229 (2024)

[2] arXiv:2403.05471

[3] arXiv:2409.03482