论文标题
克利福德·盖茨（Clifford Gates）产生的五分国家
Five-qubit states generated by Clifford gates
论文作者
论文摘要
Clifford组是由受控的Z门，相门和Hadamard Gate生成的一组门。我们会说，如果可以使用克利福德·盖茨（Clifford Gates）准备，则N Qubit State是Clifford州。这些状态称为稳定剂状态，它们以量子误差校正而产生。在本文中，我们研究了所有5个Qubit Clifford州的集合。通过使用详尽的方法，我们首先确认有19388160个州。本文的主要目的是了解受控的Z大门对5数分国家的行动的作用。考虑到这个目标，我们使用等价关系将Clifford状态分为轨道：如果当地的Clifford Gate有所不同，则两个状态是等效的。我们证明有93个轨道，我们以一种很容易看到受控Z门的效果的方式标记每个轨道。论文中呈现了CZ门在所有轨道上的作用的图和表。对于可以使用受控的Z门，Z Gate和Hadamard Gate准备的状态，对真正的Clifford 5 Qubits状态也完成了类似的工作。
The Clifford group is the set of gates generated by controlled-Z gates, the phase gate and the Hadamard gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. These states are known as the stabilizer states and they arise in quantum error correction. In this paper we study the set of all 5-qubit Clifford states. By using an exhaustive method we start by confirming that there are 19388160 states. The main goal of the paper is to understand the action of the controlled-Z gates action on the 5-qubit states. With this goal in mind, we partition the Clifford states into orbits using the equivalence relation: two states are equivalent if they differ by a local Clifford gate. We show that there are 93 orbits, and we label each orbit in such a way that it is easy to see the effect of the controlled-Z gates. Diagrams and tables explaining the action of the CZ gates on all the orbits are presented in the paper. A similar work is done for the real Clifford 5-qubits states, this is, for states that can be prepared with Controlled-Z gates, the Z gate and the Hadamard gate.
