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From graph states to two-graph states

机译：从图状态到两图状态

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摘要

The name 'graph state' is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the two-graph state, this being a generalisation of the graph state and a two-graph representation of a stabilizer state. Mathematically, the two-graph state can be viewed as a simultaneous generalisation of a binary linear code and quadratic Boolean function. It describes precisely the coefficients of the pure quantum state vector resulting from the action of a member of the local Clifford group on a graph state, and comprises a graph which encodes the magnitude properties of the state, and a graph encoding its phase properties. This description facilitates a computationally efficient spectral analysis of the graph state with respect to operations from the local Clifford group on the state, as all operations can be realised graphically. By focusing on the so-called local transform group, which is a size 3 cyclic subgroup of the local Clifford group over one qubit, and over n qubits is of size 3", we can efficiently compute spectral properties of the graph state.
机译：名称“图形状态”用于描述一类纯量子态，其对可在其上执行基于测量的量子计算的物理结构进行建模，并具有自然的图形描述。我们呈现两图状态，这是图状态的概括和稳定器状态的两图表示。在数学上，两图状态可以看作是二进制线性代码和二次布尔函数的同时推广。它精确地描述了由局部Clifford基团的成员作用于图状态而产生的纯量子状态向量的系数，并包括一个编码状态的幅值性质的图和一个编码其相位性质的图。由于所有操作都可以通过图形方式实现，因此，该描述有助于针对状态来自本地Clifford组的操作对图形状态进行计算有效的频谱分析。通过关注所谓的局部变换组，该局部变换组是局部Clifford组在一个qubit上的大小为3的循环子组，而在n qubit上在大小为3“上，我们可以有效地计算图状态的频谱特性。

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