Noisy Qudit vs Multiple Qubits : Conditions on Gate Efficiency for Enhancing Fidelity

Abstract

Today, multiple new platforms are implementing qudits, $d$-level quantum bases of information, for Quantum Information Processing (QIP). It is therefore crucial to study their efficiencies for QIP compared to more traditional qubit platforms. 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 $O(d^2/{\log }_2(d))$ of the ratio of their respective gate times in units of decoherence time. This quantity indicates how time-efficient operations on these systems are. 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. It was found that specific qudit platforms 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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