Optimal arbitrarily accurate composite pulse sequences

Abstract

Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $\epsilon$, 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 $\pi$ or $2\pi$ rotations that suppress such errors to arbitrary order $\mathcal{O}({\epsilon }^n)$ 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.

12 pages, 5 figures, submitted to Physical Review A

References in corpus (6)

• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Arbitrarily accurate composite pulses
• Concatenated composite pulses compensating simultaneous systematic errors
• Geometric Aspects of Composite Pulses
• Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors
• Nested composite NOT gates for quantum computation

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