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arXiv quant-ph/0004030quant-ph
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用几何代数和液态NMR光谱学研究量子纠错

A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy

Yehuda Sharf, David G. Cory, Shyamal S. Somaroo, Timothy F. Havel, Emanuel Knill, Raymond Laflamme

摘要:

量子纠错码能够保护包含在量子态中的信息不受由于外部扰动引起的退相干的影响。应用于NMR,量子编码不会改变正常的弛豫,而是将"数据“自旋的状态转换为涉及额外辅助自旋的多个量子相干性。这些多个量子相干性以不同的速率松弛,从而允许通过以适当的方式将它们混合在一起来近似地重建数据的原始状态。本文描述了一个简单的三比特量子码在乘积算符形式下的运算,并利用几何代数方法得到了在外部随机场中存在任意关联时的纠错后的衰减曲线.这些预测都证实了在完全相关和不相关的情况下,13 C-标记的丙氨酸的液态NMR实验,使用梯度扩散方法来实现这些理想化的退相干模型。弱极化系统中的量子纠错要求辅助自旋相对于数据自旋以伪纯态制备,这导致信号损失超过通过纠错的任何潜在增益。然而,这项研究表明,量子编码可以用来验证理论退相干机制,并提供详细的信息相关的基础NMR弛豫动力学。

英文摘要:

Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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