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

• URL: http://arxiv.org/abs/2502.05992v1
• Date: Sun, 09 Feb 2025 18:47:50 GMT
• Title: Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions
• Authors: James Keppens, Quinten Eggerickx, Vukan Levajac, George Simion, Bart Sorée,
• Abstract summary: We create and simulate the quantum circuitry for small qudit error correction codes and specifically adapted decoders. We find that the logical error rates of our simulated distance-3 codes would give less average computational errors for the higher dimensional codes.
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• Abstract: 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. We test this hypothesis by creating and simulating the quantum circuitry for small qudit error correction codes and specifically adapted decoders and compare the simulated performance with their qubit counterparts under two different noise models. We introduce an error ratio to quantify the trade-off between logical error rates and the reduction in the number of units required when using qudits. We find that the logical error rates of our simulated distance-3 codes would give less average computational errors for the higher dimensional codes, especially when the decoder can be adapted to correct more hyperedge-type errors.

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