Error-detected surgery on Iceberg codes

Abstract

We construct explicit error-detecting surgery gadgets---small systems of auxiliary qubits and checks---for the high-rate Iceberg codes $[[2N,2N-2,2]]$, to perform fault-detected measurements of logical Pauli products. The construction follows the perspective of surgery as the gauging of a logical operator, regarded as a symmetry of the code. We give a complete classification of logical Pauli operators under the permutation automorphism group of the Iceberg code, reducing the construction to one gadget per orbit, and we verify with circuit-level simulations that the gadgets are fault-detecting, with the expected post-selected logical error rate. The gadgets require reconfigurable long-range connectivity, available on platforms such as neutral-atom arrays, making an error-detected demonstration of Pauli-based computation a natural near-term experiment. The paper doubles as a self-contained introduction to gauging and code surgery, developed alongside a simple worked example.