论文标题
通用耐断层量子计算的最佳两级电路
Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation
论文作者
论文摘要
我们在Clifford+CS门集上研究了两量QU的电路，该电路由Clifford门组成，以及受控的遗相门CS = Diag（1,1,1，I）。 Clifford+CS门集是通用量子计算的通用，并且可以通过魔术状态蒸馏在大多数错误校正方案中实现其元素 - 可以实现故障。由于非克利福德门通常以容忍性的方式执行更昂贵，因此通常希望构建使用CS少量门的电路。在本文中，我们引入了一种有效，最佳的综合算法，用于两数Qubit的Clifford+CS运算符。我们的算法输入Clifford+CS运算符U，并为U输出Clifford+CS电路，该电路使用了最少数量的CS门。由于该算法是确定性的，因此可以将其与Clifford+CS运算符关联的电路视为该操作员的正常形式。我们对这些正常形式进行了明确的描述，并使用此描述来得出5log（1/epsilon）+O（1）的最差案例下限，su（4）所需的CS门数（4）。我们的工作利用了各种数学工具，这些工具可能会在耐断层量子电路的研究中找到进一步的应用。
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of 5log(1/epsilon)+O(1) on the number of CS gates required to epsilon-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.
