Trapped-ion quantum simulation of (1+1)D SU(2) lattice gauge theory via loop-string-hadron formulation

Abstract

We present a quantum simulation of the SU(2) lattice gauge theory in 1+1 dimensions with one flavor of fermions, performed using the trapped-ion Quantinuum System Model H2. This work is based on the loop-string-hadron (LSH) formulation of the gauge theory, and is distinguished by using qubits to represent both bosonic-gauge and fermionic-matter degrees of freedom. Furthermore, we access the $j=1$ electric-flux sector beyond the $j_{\max}=1/2$ truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.