论文标题
影子保利流程：涉及保利测量的MBQC中的确定性表征
Shadow Pauli Flow: Characterising Determinism in MBQCs involving Pauli Measurements
论文作者
论文摘要
我们在基于测量的量子计算（MBQC）中介绍了确定论的新表征。单向模型包括对图形表示的大纠缠状态进行局部测量。进行总体确定性计算的能力需要进行校正策略，因为每个测量值的非确定性。这种校正策略的存在取决于基础开放图，该图是对资源状态的描述以及执行的测量的基础。当在Bloch球的某些特定平面执行每个测量时，GFLOW是MBQC中鲁棒决定论的众所周知的图形表征。尽管Pauli的测量在MBQC中无处不在，但当基于测量的量子计算涉及Pauli测量值时，确定性不需要确定性。 Pauli流的设计是用Pauli测量来处理MBQC的Gflow的概括，并保证了强大的确定性，但是最近已证明它并未成为必要的条件。我们的贡献是双重的。首先，我们证明了Pauli流动实际上是较弱的确定性所必需的：鉴于开放的图，即资源状态，可以驱动确定性计算，如果它具有Pauli流。但是，保利流并不能反映特定资源状态上所有可能的校正策略，并且诸如测量顺序或计算深度之类的属性不一定会被保利流动反映。因此，为了表征完全普遍性的确定论，我们引入了一个名为Shadow Pauli Flow的进一步扩展，我们证明这是必要和足够的确定性：MBQC在且仅当其校正策略与影子Pauli流程一致时，才具有强大的确定性。此外，我们表明可以在多项式时间内计算阴影Pauli流。
We introduce a new characterisation of determinism in Measurement-Based Quantum Computing (MBQC). The one-way model consists in performing local measurements over a large entangled state represented by a graph. The ability to perform an overall deterministic computation requires a correction strategy because of the non-determinism of each measurement. The existence of such a correction strategy depends on the underlying open graph, which is a description of the resource state together with the basis of the performed measurements. GFlow is a well-known graphical characterisation of robust determinism in MBQC when every measurement is performed in some specific planes of the Bloch sphere. While Pauli measurements are ubiquitous in MBQC, GFlow fails to be necessary for determinism when a measurement-based quantum computation involves Pauli measurements. Pauli Flow was designed as a generalisation of GFlow to handle MBQC with Pauli measurements, and guarantees robust determinism, however, it has been shown more recently that it fails to be a necessary condition. Our contribution is twofold. First, we demonstrate that Pauli flow is actually necessary for robust determinism in a weaker sense: given an open graph, i.e. a resource state, a deterministic computation can be driven iff it has a Pauli flow. However, the Pauli flows do not reflect all the possible correction strategies over a particular resource state, and properties like measurement order or computational depth are not necessarily reflected by a Pauli flow. Thus, to characterise determinism in full generality, we introduce a further extension called Shadow Pauli Flow that we prove necessary and sufficient for robust determinism: An MBQC is robustly deterministic if and only if its correction strategy is consistent with a Shadow Pauli flow. Furthermore, we show that Shadow Pauli flow can be computed in polynomial time.
