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arXiv · 1307.2211

Optimal arbitrarily accurate composite pulse sequences

Guang Hao Low·Theodore J. Yoder·Isaac L. Chuang
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Abstract

Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $ε$, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of $L$ primitive $π$ or $2π$ rotations that suppress such errors to arbitrary order $\mathcal{O}(ε^{n})$ on arbitrary initial states. Optimality is demonstrated by proving an $L=\mathcal{O}(n)$ lower bound and saturating it with $L=2n$ solutions. Closed-form solutions for arbitrary rotation angles are given for $n=1,2,3,4$. Perturbative solutions for any $n$ are proven for small angles, while arbitrary angle solutions are obtained by analytic continuation up to $n=12$. The derivation proceeds by a novel algebraic and non-recursive approach, in which finding amplitude error correcting sequences can be reduced to solving polynomial equations.

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Guang Hao Low, Theodore J. Yoder, Isaac L. Chuang. 2014-01-15. Optimal arbitrarily accurate composite pulse sequences. https://doi.org/10.1103/physreva.89.022341

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