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arXiv:1303.1745 · Physical Review A

Designing short robust not gates for quantum computation

Jonathan A. Jones

Published May 20, 2013• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.052317

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[Abstract] Quantum operations robust against random noise and systematic errors are essential ingredients in the quantum control. We have theoretically studied such robust quantum operations against the errors, that consist of several elementary operations and are called composite quantum gates. In this article, we experimentally discuss the robustness of various composite quantum gates by using NMR (Nuclear Magnetic Resonance) that is one of the most familiar quantumly controlled systems. [概要] 量子制御には乱雑なノイズや系統的なエラーの影響を受け難い量子操作が必要である。我々は今までエラー耐性を持つ量子操作（複数の基本的な量子操作を組み合わせた複合量子ゲート）の理論的な研究を主に行ってきた。本稿では、最も身近な量子制御であるNMR（核磁気共鳴）を用いて、様々な複合量子ゲートのエラー耐性を実験的に調べる。

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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.
We propose various composite πππ-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linear length scaling, indicating an efficient construction of them with arbitrary accuracy.
High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit heightened sensitivity to errors. We investigate such sensitive quantum gates, which, beyond their established use in nuclear magnetic resonance spectroscopy and polarization optics, may offer significant utility in the other areas where selectivity, filtering, sensing, localization, or addressing properties are of interest. Utilizing the composite pulses technique, we derive three fundamental quantum gates with narrowband and passband characteristics—the () gate, the gate, and gates enabling arbitrary rotations. To systematically design these composite pulse sequences, we introduce the SU(2), modified-SU(2), and regularization random search methodologies. These approaches demonstrate superior performance compared to established sequences in the literature, including NB1, SK1, and PB1.
[Abstract] Quantum operations robust against random noise and systematic errors are essential ingredients in the quantum control. We have theoretically studied such robust quantum operations against the errors, that consist of several elementary operations and are called composite quantum gates. In this article, we experimentally discuss the robustness of various composite quantum gates by using NMR (Nuclear Magnetic Resonance) that is one of the most familiar quantumly controlled systems. [概要] 量子制御には乱雑なノイズや系統的なエラーの影響を受け難い量子操作が必要である。我々は今までエラー耐性を持つ量子操作（複数の基本的な量子操作を組み合わせた複合量子ゲート）の理論的な研究を主に行ってきた。本稿では、最も身近な量子制御であるNMR（核磁気共鳴）を用いて、様々な複合量子ゲートのエラー耐性を実験的に調べる。