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.

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• Quantum circuits
• Quantum computation
• Quantum error correction
• Quantum simulation