Individually Addressed Logical Pauli Measurements by QLDPC Surgery on a Trapped Ion Quantum Computer

Abstract

Quantum low-density parity check (QLDPC) codes may lead to order-of-magnitude reductions in the qubit overhead required for fault-tolerant quantum computation. Achieving this improved overhead requires logical operations that selectively address individual logical qubits encoded within multi-qubit code blocks. Recently proposed architectures achieve this through QLDPC surgery, in which non-destructive Pauli measurements are performed using ancillary ''gadget'' systems transiently entangled with the code block, generalising lattice surgery. Here we implement QLDPC surgery on a [[10,2,3]] generalised bicycle code using Quantinuum's H2-2 trapped ion processor. A single-round surgery measurement using seven gadget qubits measures the $\bar{X}_1$ operator with a 0.72 [0.32, 1.41]% (95% credible interval) error rate and agrees with subsequent transversal measurement with 1.03 [0.60, 1.65]% error. Decoding across three rounds of syndrome extraction suppresses the gadget measurement error, reducing the error rate to below 0.26%. The syndrome after surgery confirms return to the code space and the unaddressed ''spectator'' qubit is preserved with error 0.21 [0.04, 0.67]% during the three-round measurement. We further demonstrate composition of conjugate basis gadgets by sequentially measuring $\bar{X}_1$ then $\bar{Z}_2$, reusing the gadget qubits, and obtain a 1.12 [0.60, 1.94]% error in the $\bar{Z}_2$ measurement. These results constitute a hardware validation of the generalised surgery primitive underlying Pauli-based computing for QLDPC architectures.