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arXiv · 2604.25807

Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences

Domenico D'Alessandro·Phattharaporn Singkanipa·Daniel Lidar
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Abstract

Universally robust dynamical decoupling (UR$n$) sequences were proposed to compensate pulse imperfections arising from arbitrary experimental parameters while achieving high-order error suppression with only a linear increase in the number of pulses. Although their performance was supported by analytical arguments, numerical simulations, and experiments, a complete mathematical proof of the claimed order of error compensation has been absent. In this work, we present a rigorous proof for UR$n$ DD sequences with even $n$. Using a series expansion of a quantity whose modulus is the fidelity $F$, we derive necessary and sufficient conditions for the cancellation of its coefficients up to, but not including, order $n$. The UR$n$ phase prescription satisfies these conditions, and therefore $1-F=O(\epsilon^n)$. Our results establish the UR$n$ construction on firm analytical grounds and clarify the structure responsible for its high-order robustness.

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Domenico D'Alessandro, Phattharaporn Singkanipa, Daniel Lidar. 2026-04-28. Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences. https://arxiv.org/abs/2604.25807

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