As qubit-based platforms face near-term technical challenges in terms of scalability, qudits, d-level bases of quantum information, are being implemented in multiple platforms as an alternative for Quantum Information Processing (QIP). We compare the infidelity scalings of single qudit and multiqubit systems within identical Hilbert space dimensions and noisy environments in the Lindblad formalism. We find them to be gate-independent to first-order and present an analytically-derived critical curve \(({d}^{2}-1)/3{\log }_{2}(d)\) that benchmarks the operational time efficiency of qudits and qubits relative to their decoherence times. This comparison reveals conditions under which qudits offer competitive gate efficiencies compared to leading qubit platforms. Our findings, supported by numerical simulations testing the applicability and limits of the linear response formalism, highlight the relevance of qudits in near-term QIP. This provides a benchmark for evaluating qudit platforms, specifically those with lower dimensionality, in terms of their operational efficiency relative to the qubit state-of-the-art.

由于基于量子位的平台在可扩展性方面面临近期技术挑战，量子信息的 d 级基础正在多个平台中实现，作为量子信息处理 (QIP) 的替代方案。我们比较了 Lindblad 形式主义中相同希尔伯特空间维度和噪声环境中单量子位和多量子位系统的不保真缩放。我们发现它们与一阶门无关，并提出了一条分析得出的临界曲线 \(({d}^{2}-1)/3{\log }_{2}(d)\) 进行基准测试量子位和量子位相对于其退相干时间的运行时间效率。这一比较揭示了与领先的量子位平台相比，量子位提供有竞争力的门效率的条件。我们的研究结果得到了测试线性响应形式主义的适用性和局限性的数值模拟的支持，强调了 qudits 在近期 QIP 中的相关性。这为评估 qudit 平台（特别是那些低维平台）相对于最先进的量子位的运行效率提供了基准。