Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913069633896448 |
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| author | D'Alessandro, Domenico Singkanipa, Phattharaporn Lidar, Daniel |
| author_facet | D'Alessandro, Domenico Singkanipa, Phattharaporn Lidar, Daniel |
| contents | 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 $1-F=O(ε^n)$. Our results establish the UR$n$ construction on firm analytical grounds and clarify the structure responsible for its high-order robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences D'Alessandro, Domenico Singkanipa, Phattharaporn Lidar, Daniel Quantum Physics Information Theory 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 $1-F=O(ε^n)$. Our results establish the UR$n$ construction on firm analytical grounds and clarify the structure responsible for its high-order robustness. |
| title | Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2604.25807 |