Nuclear-magnetic-resonance quantum calculations of the Jones polynomial.
Nuclear-magnetic-resonance quantum calculations of the Jones polynomial.
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DOI：
10.1103/physreva.81.032319
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发表时间：
2010-03
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影响因子：
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通讯作者：
R. Marx;A. Fahmy;L. Kauffman;S. Lomonaco;A. Spörl;N. Pomplun;T. Schulte-Herbrüggen;J. Myers;S. Glaser
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作者：
R. Marx;A. Fahmy;L. Kauffman;S. Lomonaco;A. Spörl;N. Pomplun;T. Schulte-Herbrüggen;J. Myers;S. Glaser
量子计算机理论上可解决的问题库最近扩展到包括结不变量的近似计算，特别是琼斯多项式。然而，这种评价的实验实施涉及许多已知的实验挑战。在这里，我们提出了小规模的近似评价的琼斯多项式的核磁共振（NMR）的实验结果，此外，我们展示了如何摆脱NMR方法，采用伪纯状态的局限性。具体来说，我们使用两个自旋1/2核的天然丰度氯仿和应用一系列的酉变换代表三叶结，8字结，和Borromean环。在测量了每种情况下分子的核自旋状态之后，我们能够估计每个结的琼斯多项式的值。
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.