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arXiv:quant-ph/0301019 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Robust quantum information processing with techniques from liquid–state NMR

Jonathan A. Jones

Published Jul 15, 2003• 19 citations
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Abstract

While nuclear-magnetic-resonance (NMR) techniques are unlikely to lead to a large-scale quantum computer, they are well suited to investigating basic phenomena and developing new techniques. Indeed, it is likely that many existing NMR techniques will find uses in quantum information processing. Here I describe how the composite-rotation (composite-pulse) method can be used to develop quantum logic gates which are robust against systematic errors.

DOI
10.1098/rsta.2003.1212

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While nuclear-magnetic-resonance (NMR) techniques are unlikely to lead to a large-scale quantum computer, they are well suited to investigating basic phenomena and developing new techniques. Indeed, it is likely that many existing NMR techniques will find uses in quantum information processing. Here I describe how the composite-rotation (composite-pulse) method can be used to develop quantum logic gates which are robust against systematic errors.
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.
The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on the BB1 family of composite rotations have been experimentally demonstrated in a variety of systems, but little study has been made of their application in extended computations, and there has been no experimental study of the corresponding robust two qubit gates to date. Here we describe an application of robust gates to nuclear magnetic resonance studies of approximate quantum counting. We find that the BB1 family of robust gates is indeed useful, but that the related NB1, PB1, B4, and P4 families of tailored logic gates are less useful than initially expected.
[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。
Quantum computers exploit quantum mechanical phenomena as resources to process information.They are therefore far more vulnerable to errors than their classical counterparts.The main obstacle to the practical realization of a working large-scale quantum computer is decoherence, i.e., the process by which a quantum system decays to a classical state through interaction with the environment.We herein discuss two techniques to implement robust quantum information processing, and report on their implementation in a liquid state NMR Quantum Computing experiment.We describe a method to implement a two-qubit gate between spins 2 and 3 of a three-spin linear chain molecule by applying a soft pulse to spin 1, with appropriate choices of the rf-field amplitude ω 1 and duration τ [1].The Bloch-Siegert effect for such a soft pulse is negligible in general, which makes NMR pulse programming and quantum gates design much simpler than with conventional hard π-pulses; it also makes this method suitable for use with both homo-and heteronuclear molecules.We then discuss a simple Operator Quantum Error Correction (OQEC) scheme with three qubits [2].This scheme provides the simplest possible Noiseless Subsystem, in terms of the number of CNOT gates, that is robust against (restricted) fully correlated noise.We demonstrated our OQEC scheme experimentally using a three-qubit NMR Quantum Computer, in which the ancillae are in the maximally mixed state.In this experiment, we made practical use of the soft pulse technique [1] to implement the two-qubit gates in the pulse sequences realizing encoding and decoding operations.