Digitizing Gauge Invariant Interactions, II: Quantum Algorithms for SU(2) Gauge Fields and Matter in (1+1)D

We present scalable quantum algorithms to simulate (1+1)D SU(2) lattice gauge theory in both near-term and far-term quantum resource scenarios. In these scenarios, we compare the cost of the algorithms, along with their development and analysis to that of algorithms for simulating U(1) lattice gauge theory in (1+1)D. This presentation focuses on the gauge-fermion interaction ("hopping") terms, for which the generalization from U(1) to SU(2) is the most involved. We use the block-diagonalized interaction terms for both U(1) and SU(2), as discussed in J. Stryker's presentation, and give quantum algorithms which implement them while conserving the largest possible set of commuting gauge constraints.