Qudit vs. qubit: Simulated performance of error-correction codes in higher dimensions

Qudits can be described by a state vector in a q-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using qudits rather than qubits might entail less overhead. In this work, we investigate the viability of qudits in error-correction codes by creating and simulating the quantum circuitry for the smallest qudit error-correction code with a multidimensional circuit-level noise model and specifically adapted decoders. After introducing a flag qudit to protect the code from hook errors, comparable error thresholds of the order of 10-4 are obtained for qudits of dimensions 2, 3, and 5.