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arXiv quant-ph/0309121quant-phcs.ET
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量子软件的可重用性

Quantum Software Reusability

Andreas Klappenecker, Martin Roetteler

AI总结:

针对给定酉矩阵难以寻找高度优化量子电路的问题,提出一种通过重用和组合已有高效量子电路来系统化构建新电路的方法,并基于群的表示矩阵线性组合实现,成功推导出离散哈特利变换等高效电路。

摘要:

高效量子电路的设计是量子计算中的一个重要问题。对于给定的酉矩阵,寻找一个高度优化的量子电路通常是一项艰巨的任务。我们提出了一种量子电路设计方法,该方法具有以下独特特征:它允许通过重用和组合一组高度优化的量子电路,以系统化的方式构建高效的量子电路。具体而言,该方法通过实现一个群的表示矩阵的线性组合,来为给定的酉矩阵构建量子电路,而这些表示矩阵已具有已知的高效量子电路。我们通过为离散哈特利变换和分数阶傅里叶变换推导出极其高效的量子电路,来论证并说明该方法。这种设计方法坚实的数学基础使得能够对所得电路给出有意义且自然的解释。我们通过给出已知隐形传态电路的自然解释来展示这一方面。

英文摘要:

The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that has the following unique feature: It allows to construct efficient quantum circuits in a systematic way by reusing and combining a set of highly optimized quantum circuits. Specifically, the method realizes a quantum circuit for a given unitary matrix by implementing a linear combination of representing matrices of a group, which have known fast quantum circuits. We motivate and illustrate this method by deriving extremely efficient quantum circuits for the discrete Hartley transform and for the fractional Fourier transforms. The sound mathematical basis of this design method allows to give meaningful and natural interpretations of the resulting circuits. We demonstrate this aspect by giving a natural interpretation of known teleportation circuits.

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