Experiments with the four-dimensional surface code on a quantum charge-coupled device quantum computer

Single-shot quantum error correction has the potential to speed up quantum computations by removing the need for multiple rounds of syndrome extraction to be fault-tolerant. By using Quantinuum's H2 trapped-ion quantum computer, we implement the [33,1,4] four-dimensional (4D) surface code and perform an experimental demonstration of single-shot quantum error correction with bare ancilla qubits. We conduct memory experiments comparing the two-dimensional (2D) and 4D surface codes and find that, despite differences in qubit use and syndrome extraction circuit depth, the 4D surface code matches or outperforms the 2D surface code in both the fault-tolerant and single-shot regimes.