The recent success of error detecting codes points toward their potential application to fault-tolerant simulations of nature. In this work, we examine the utility of sparse error detection for simulating lattice gauge theories using quantum computers. In particular, we study the time evolution of the lattice Schwinger model embedded into the Iceberg code family, [[N+2, N, 2]], as well as the Hypercube code family, [[2^N, N, 2]]. The lattice of electrons and positrons in the axial gauge is embedded into a single code block or into multiple code blocks, and this work finds that large codeblocks are advantageous in the absence of connectivity constraints. Noisy classical simulations with realistic near-term error rates, infrequent syndrome measurements and physics-aware postselection are found to improve observable estimation. Under realistic noise rates for near-term quantum computers, this work finds that sparse error detection in quantum simulations has the potential to improve accuracy of observable estimation. Additional rounds of error detection are found to systematically drive errors in observables to the noise floor set by the code. These findings suggest that incorporating minimal implementations of fault tolerance in the near-term will enhance the performance of quantum simulations in nuclear physics and high-energy physics.

This work was supported by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science. Support is also acknowledged from the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator (Award No. DE-SCL0000121). This work was also supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, Grant No. DE-FG02-97ER-41014 (UW Nuclear Theory). S.G. was supported in part by a Feodor Lynen Research fellowship of the Alexander von Humboldt foundation. This work was also supported, in part, through the Department of Physics and the College of Arts and Sciences at the University of Washington. This work was enabled, in part, by the use of advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system at the University of Washington. We acknowledge the use of Claude for code development.