Phase map decompositions for unitaries
Phase map decompositions for unitaries
复制标题
酉矩阵的相图分解
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
E. Kashefi
中科院分区：
文献类型：
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作者：
N. D. Beaudrap;V. Danos;E. Kashefi
我们提出了 C^2 张量幂上酉映射的通用分解，引入了“相位图”的关键概念，并研究了如何使用这种分解直接在基于测量的量子计算模型中实现酉映射。具体来说，我们展示了如何从这样的分解中提取匹配的纠缠图状态（带有输入）以及一组测量角度（如果有）。接下来，我们检查获得的图状态是否验证“流”条件，这保证了执行顺序，使得模式的相关测量和校正产生确定性结果。使用流的图论表征，我们可以确定是否可以在多项式时间内为图状态构造流。这种方法产生了一个算法过程，当它成功时，可以为给定的酉生成有效的模式。
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based model for quantum computing. Specifically, we show how to extract from such a decomposition a matching entangled graph state (with inputs), and a set of measurements angles, when there is one. Next, we check whether the obtained graph state verifies a "flow" condition, which guarantees an execution order such that the dependent measurements and corrections of the pattern yield deterministic results. Using a graph theoretic characterization of flows, we can determine whether a flow can be constructed for a graph state in polynomial time. This approach yields an algorithmic procedure which, when it succeeds, may produce an efficient pattern for a given unitary.