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arXiv:quant-ph/0008034

Resonance Offset Tailored Pulses for NMR Quantum Computation

Holly K. Cummins, Jonathan A. Jones

Published Aug 7, 2000• 1 citation
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Abstract

We describe novel composite pulse sequences which act as general rotors and thus are suitable for nuclear magnetic resonance (NMR) quantum computation. The Resonance Offset Tailoring To Enhance Nutations (ROTTEN) approach permits perfect compensation of off-resonance errors at two selected frequencies placed symmetrically around the frequency of the RF source.

DOI
10.48550/arxiv.quant-ph/0008034

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We describe novel composite pulse sequences which act as general rotors and thus are suitable for nuclear magnetic resonance (NMR) quantum computation. The Resonance Offset Tailoring To Enhance Nutations (ROTTEN) approach permits perfect compensation of off-resonance errors at two selected frequencies placed symmetrically around the frequency of the RF source.
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We implement an ensemble quantum counting algorithm on three NMR spectrometers with 1H resonance frequencies of 500, 600 and 750 MHz. At higher frequencies, the results deviate markedly from naive theoretical predictions. These systematic errors can be attributed almost entirely to off-resonance effects, which can be substantially corrected for using fully-compensating composite rotation pulse sequences originally developed by Tycko. We also derive an analytic expression for generating such sequences with arbitrary rotation angles.
We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in nuclear magnetic resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180\ifmmode^\circ\else\textdegree\fi{} rotation in a two spin system. Finally, we show how these two approaches can be combined to produce more accurate frequency selective rotations.
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.
Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses-one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system-have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.