Noisy Qudit vs Multiple Qubits : Conditions on Gate Efficiency
arXiv (Cornell University)(2023)
摘要
As qubit-based platforms face near-term technical challenges in terms of scalability, qudits, $d$-level quantum bases of information, are being implemented in multiple platforms as an alternative for Quantum Information Processing (QIP). It is, therefore, crucial to study their efficiencies for QIP compared to more traditional qubit platforms, specifically since each additional quantum level represents an additional source of environmental coupling. We present a comparative study of the infidelity scalings of a qudit and $n$-qubit systems, both with identical Hilbert space dimensions and noisy environments. The first-order response of the Average Gate Infidelity (AGI) to the noise in the Lindblad formalism, which was found to be gate-independent, was calculated analytically in the two systems being compared. This yielded a critical curve $(d^2-1)/3\log_2(d)$ of the ratio of their respective figure of merits, defined as the gate time in units of decoherence time. This quantity indicates how time-efficient operations on these systems are relative to decoherence timescales, and the critical curve is especially useful for precisely benchmarking qudit platforms with smaller values of $d$. The curve delineates regions where each system has a higher rate of increase of the AGI than the other. This condition on gate efficiency was applied to different existing platforms. Specific qudit platforms were found to possess gate efficiencies competitive with state-of-the-art qubit platforms. Numerical simulations complemented this work and allowed for discussion of the applicability and limits of the linear response formalism.
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关键词
multiple qubits,gate efficiency
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