Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers. We introduce and study the vector space of linear dependencies of n-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in n. We construct elegant bases of linear dependencies of constant size three. Critically, our sparse bases can be computed without first compiling a dictionary of all n-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

中文翻译：

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优化量子态稳定器分解的基础


稳定态在量子计算理论中发挥着核心作用。例如，它们用于对最常见的量子纠错方案中的计算基础状态进行编码。任意量子态承认许多稳定剂分解：表示为稳定态叠加的方式。了解稳定器分解的结构在验证和模拟近期量子计算机方面具有重要应用。我们介绍并研究线性相关性的向量空间n -量子位稳定器状态。这些空间具有包含向量的规范基，其大小在n 。我们构建了大小恒定为三的线性依赖的优雅基础。至关重要的是，我们的稀疏基数可以在不首先编译所有基数的字典的情况下进行计算。 n -量子位稳定器状态。我们利用它们来显式计算比现有技术可行的更多量子位的状态稳定范围。最后，我们描述了未来的应用，以改善魔态稳定等级的理论界限。