Quantum error-detecting codes offer a near-term path for improving the performance of quantum simulations on noisy hardware. Using IBM’s superconducting quantum computer ibm boston, we show that partially fault-tolerant encoded quantum simulations of the Ising model in 1+1D and 2+1D outperform their unencoded counterparts in estimating local observables. To represent 42 logical qubits on the heavy-hex quantum processor, 21 blocks of the [[4, 2, 2]] Iceberg code and up to 136 physical qubits are used. By pairing fault-tolerant syndrome extraction with non-fault-tolerant logical operations, this scheme preserves many of the benefits of error detection while avoiding the overhead typically required for a fully fault-tolerant logical gate set. The encoding’s square logical connectivity, together with the freedom to place logical qubits within each block, enables simulations of a 2D spatial lattice with lower circuit depth than an unencoded implementation would require. We introduce Observable-Ranked Postselection, a selective-filtering technique based on syndrome correlations that recovers reliable results without the prohibitive shot loss of full syndrome postselection. Under the cumulative effect of device errors, this encoding improves local-observable accuracy over the unencoded baseline by 2-6% at intermediate times in 1+1D simulations, growing with circuit depth to over 200% in 2+1D at the latest times studied.

We would like to thank John Preskill for helpful discussions. This work was supported, in part, 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, in part, by the Department of Physics and the College of Arts and Sciences at the University of Washington, and 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. We acknowledge the use of IBM Quantum Credits for this work. The views expressed are those of the authors, and do not reflect the official policy or position of IBM or the IBM Quantum team. The Quimb library was used for tensor network simulations, and QuSpin was used for exact diagonalization computations.