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arXiv:1508.02983 · Scientific Reports

Concatenated Composite Pulses Applied to Liquid-State Nuclear Magnetic Resonance Spectroscopy

Masamitsu Bando, Tsubasa Ichikawa, Yasushi Kondo, Nobuaki Nemoto, Mikio Nakahara, Yutaka Shikano

Published Feb 7, 2020• 11 citations
arXivHTMLPDF

Abstract

The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.

DOI
10.1038/s41598-020-58823-9

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The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.
In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.
In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.
Composite pulses, originally developed in nuclear magnetic resonance (NMR), have found widespread use in experimental quantum information processing (QIP) to reduce the effects of systematic errors. Most pulses used so far have simply been adapted from existing NMR designs, and while techniques have been developed for designing composite pulses with arbitrary precision, the results have been quite complicated and have found little application. Here, I describe techniques for designing short but effective composite pulses to implement robust not gates, bringing together existing insights from NMR and QIP, and present some composite pulses.
Composite pulse sequences designed for nuclear magnetic resonance experiments are currently being applied in many quantum information processing technologies. We present an analysis of a family of composite pulse sequences used to address systematic pulse-length errors in the execution of quantum gates. It has been demonstrated by Cummins et al. [Phys. Rev. A 67, 042308 (2003)] that for this family of composite pulse sequences, the fidelity of the resulting unitary operation compared with the ideal unitary operation is $1\ensuremath{-}C{ϵ}^{6}$, where ϵϵϵ is the fractional error in the length of the pulse. We derive an exact expression for the sixth-order coefficient CCC and from this deduce conditions under which this sixth-order dependence is observed. We also present pulse sequences which achieve the same fidelity.