发表机构
Université de Lorraine; CNRS; Inria; École des Mines, Université de Lorraine; Institute of Theoretical Physics, Leibniz University Hannover（洛林大学; 法国国家科学研究中心; 法国国家计算机科学研究所; 洛林大学国立高等矿业学院; 汉诺威莱布尼茨大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无标签开放图上的测量型量子计算，提出一种在O(n^3)时间内同时确定测量标签与兼容gflow的算法，并处理顺序约束，证明输入输出数相等时标签唯一，且可扩展输入而不破坏gflow。
AI 中文摘要
基于测量的量子计算（measurement-based quantum computing）的单向模型（one-way model）通过对资源图态（resource graph state）进行连续自适应的单量子比特测量来实现计算。该模型具有实际应用，特别是在光子学中，并且作为理论工具也很有用，例如用于优化。Gflow 是在适当意义上确定性地实现某些单向计算的必要且充分条件；它也用于从单向模型到量子电路的高效转换。对于 $n$ 个量子比特上的计算，可以在 $\mathcal{O}(n^3)$ 时间内找到 gflow。在这里，我们考虑由无标签开放图（unlabelled open graph）给出的不完全指定的计算：图态以及输入和输出量子比特已知，但测量尚未固定。我们给出了一种算法，该算法识别测量标签和兼容的 gflow，并在 $\mathcal{O}(n^3)$ 时间内运行，严格推广了先前的方法。新算法还可以处理测量顺序的限制，并且仅返回与这些约束兼容的解决方案。我们还证明了如果开放图具有相等数量的输入和输出，则它至多有一个与 gflow 兼容的标签；并展示了如何为尚未具有最大数量的开放图识别额外的输入，而不会破坏现有的 gflow。最后，我们展示了输入或潜在输入与计算中的信息流之间的关系。
英文摘要
The one-way model of measurement-based quantum computing implements computations via successive adaptive single-qubit measurements on a resource graph state. This model has practical applications, particularly in photonics, and it is also useful as a theoretical tool e.g. for optimisation. Gflow is a necessary and sufficient condition for implementing certain one-way computations deterministically (in a suitable sense); it is also used in efficient translations from the one-way model to quantum circuits. For a computation on $n$ qubits, a gflow can be found in $\mathcal{O}(n^3)$ time. Here, we consider an incompletely specified computation given by an unlabelled open graph: the graph state as well as the input and output qubits are known, but the measurements have not yet been fixed. We give an algorithm that identifies a measurement labelling and a compatible gflow, and runs in $\mathcal{O}(n^3)$, strictly generalising the previous approach. The new algorithm can also handle restrictions on the order of the measurements and returns only solutions compatible with these constraints. We additionally prove that if an open graph has equal numbers of inputs and outputs, it has at most one labelling compatible with gflow; and show how to identify additional inputs for an open graph that does not yet have the maximal number, without breaking an existing gflow.
Comments28+6 pages
