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In the near-future noisy intermediate-scale quantum (NISQ) era of quantumcomputing technology, applications of quantum computing will be limited tocalculations of very modest scales in terms of the number of qubits used. Theneed to represent numeric quantities using limited resources leads todigitization errors which must be taken into account. As a first step towardsquantum simulations of realistic high-energy physics problems, we exploreclassically the effects of digitizing elements of the $\mathrm{SU}(2)$ gaugegroup to a finite set. We consider several methods for digitizing the group,finding the best performance from an action-preserving projection onto a mesh.Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to representeach $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of$10\%$ in short-distance observables and $2\%$ in long-distance observables.Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can berepresented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$$\mathrm{SU}(2)$ lattice could be simulated with no more than$\mathcal{O}(10^5)$ (qu)bits. Our results on digitization are also of interestas a form of lossy compression that could be used in high-performance classicalcomputing to alleviate communications bottlenecks.

Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers