论文标题
通过Pauli测量的MBQC模式的完整保留流程重写规则
Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements
论文作者
论文摘要
在基于测量的量子计算（MBQC）的单向模型中，计算通过对某些标准资源状态的测量进行。所谓的流动条件可确保总体计算在适当的意义上是确定性的，保利流是其中最笼统的。在保留流量存在的同时，有关重写MBQC模式的现有工作集中在减少量子数量的重写上。 在这项工作中，我们表明，引入了新的Z测量量子位，并连接到现有量子位的任何子集，都保留了Pauli Flow的存在。此外，我们为稳定器ZX-DIAGRAS提供了独特的规范形式，该形式受Hu＆Khesin最近工作的启发。我们证明，任何具有Pauli流量的MBQC样稳定器ZX-DIAGRAM都可以仅使用保留Pauli流的存在的规则将其重写为这种规范形式，并且这些规则都可以逆转，同时也可以保留Pauli流的存在。因此，我们对具有Pauli流量的MBQC样稳定器ZX-DIAGRAM具有完整的图形重写。
In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits. In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin. We prove that any MBQC-like stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow, and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.
