Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques

Journal Article · 22 December 2024 · PRX Quantum

DOI: https://doi.org/10.1103/prxquantum.5.040347 · OSTI ID:2483714

Rhodes, Mason L.  ^[1]; Kreshchuk, Michael  ^[2]; Pathak, Shivesh  ^[3]

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1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); University of New Mexico, Albuquerque, NM (United States)
2. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Phasecraft Inc., Washington, DC (United States)
3. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2), and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find a reduction of up to 25 orders of magnitude in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods, which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first-principles quantum simulation of chemistry.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE; USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP); USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: AC02-05CH11231; NA0003525
• OSTI ID: 2483714
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 4 Vol. 5; ISSN 2691-3399
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English