Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques

Significant progress in quantum simulation of high-energy physics (HEP) has been made by developing Hamiltonian formulations suitable for quantum computation, alongside performing near-term explorations and benchmarks. However, the complexity of realistic HEP models—characterized by a large number of degrees of freedom and complex form of interactions—indicates that simulating practical problems on fault-tolerant quantum devices may demand fundamentally different algorithms than those used for near-term simulations. This observation is confirmed by substantial resource requirements identified in studies to date.

Drawing inspiration from recent algorithmic advances in quantum chemistry—where ab initio simulation resource estimates have been reduced from ~10^40..50 to ~10^10...15 T-gates over the past decade—we demonstrate in arXiv:2405.10416 that similar cost reductions are achievable in HEP simulations. These improvements hinge on leveraging the Hamiltonian’s structure (e.g., via local fermion-to-qubit mappings) and using advanced simulation techniques, commonly termed "post-Trotter" methods or "qubitization." In particular, the most significant resource reductions were achieved using interaction picture simulations via the truncated Dyson series algorithm and construction of block encodings based on sparse oracles. Our findings indicate that, with careful optimization, the resource requirements for quantum simulation of lattice gauge theories can approach those found in quantum chemistry and materials science, bringing them to the ranges discussed in current hardware proposals.