论文标题
没有符号组的稳定电路还原稳定电路
Reducing stabilizer circuits without the symplectic group
论文作者
论文摘要
我们首先研究稳定稳定器电路的亚组结构。然后，我们将结果应用于稳定器电路的两种正常形式。这些形式是通过使用Clifford组中的简单共轭规则归纳来计算的，我们的算法不依赖于符号组中的特殊分解。第一种正常形式具有形状的CX-CZ-Z-X-H-CZ-p-H，其中CX（resp。CZ）表示一层CNOT（resp。Controted-Z）门，P一层相位门，X（eves.z），X（resp。Z）一层Pauli-X（resp。pauli-Z）门。然后，我们用CNOT门替换大多数受控的-Z门，以获得第二种正常形式的P-CX-CZ-CX-CX-Z-Z-H-CZ-CZ-CX-p-H。在第二种形式中，两个受控的Z层具有深度1，因此最多包含N受控的Z门。我们还考虑了稳定态和图形状态的正常形式。最后，我们对经典和量子计算机进行了一些测试，以便通过实验表明这些正常形式的实用性以减少稳定器电路的栅极计数。
We start by studying the subgroup structures underlying stabilizer circuits. Then we apply our results to provide two normal forms for stabilizer circuits. These forms are computed by induction using simple conjugation rules in the Clifford group and our algorithms do not rely on a special decomposition in the symplectic group. The first normal form has shape CX-CZ-P-Z-X-H-CZ-P-H, where CX (resp. CZ) denotes a layer of CNOT (resp. controlled-Z) gates, P a layer of phase gates, X (resp. Z) a layer of Pauli-X (resp. Pauli-Z) gates. Then we replace most of the controlled-Z gates by CNOT gates to obtain a second normal form of type P-CX-CZ-CX-Z-X-H-CZ-CX-P-H. In this second form, both controlled-Z layers have depth 1 and together contain therefore at most n controlled-Z gates. We also consider normal forms for stabilizer states and graph states. Finally we carry out a few tests on classical and quantum computers in order to show experimentally the utility of these normal forms to reduce the gate count of a stabilizer circuit.
