论文标题
串联的三分之一代码的优点
The advantage of the concatenated three-qubit codes
论文作者
论文摘要
在这项工作中，针对一般独立噪声的有效量子误差校正方案是用三个QUIT代码构建的。串联规则根据代码的错误校正功能总结。这些代码不仅发挥了纠正错误的作用，而且还起到有效渠道的两极作用。对于任何独立的噪声，可以根据串联规则构建最合适的错误校正协议。使用串联的三度代码的最重要方面是通过非理想的门操作实现量子误差校正，因为三quit代码的误差校正方案是简单且模块化的。例如，对于使用初始通道保真度为0.9的振幅阻尼噪声，当使用4级串联的量子误差纠正与三个Qubit代码时，有效的通道保真度可以达到0.94731（或带有理想量子门操作的0.961634）。当准确率为0.9995时，带有三分之一代码的协议需要81吨和366个量子门操作。同时，当将3个级别串联量子误差与五量级代码使用时，有效的通道保真度只能达到0.922798（或带有理想量子门操作）的0.922798（或0.975488）。当准确率为0.9995时，带有五分位代码的协议需要125 QUAT和1147量子门操作。经过的物理资源是通过意识到三量量子误差校正，协议具有较高的容错阈值，并且复杂性没有增加而花费的物理资源的倍数。因此，我们认为这将有助于实现物理系统中的量子错误纠正。
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the codes. The codes not only play the role of correcting errors, but the role of polarizing the effective channel. For any independent noise, the most suitable error-correction protocol can be constructed based on the rules of concatenation. The most significant aspect of using the concatenated three-qubit codes is to realize quantum error-correction with the non-ideal gate operations, because the error-correction schemes of the three-qubit codes are simple and modular. For example, for the amplitude damping noise with the initial channel fidelity 0.9, the effective channel fidelity can reach 0.94731 (or 0.961634 with the ideal quantum gate operations) when using the 4 levels concatenated quantum error-correction with the three-qubit codes. The protocol with the three-qubit codes needs 81 qubits and 366 quantum gate operations when the accuracy rate is 0.9995. Meanwhile, when using the 3 levels concatenated quantum error-correction with the five-qubit code, the effective channel fidelity can only reach 0.922798 (or 0.975488 with the ideal quantum gate operations). The protocol with the five-qubit code needs 125 qubits and 1147 quantum gate operations when the accuracy rate is 0.9995. The physical resources costed is multiple of the physical resources costed by realizing the three-qubit quantum error-correction, the protocol has a higher fault tolerance threshold, and no increase in complexity. So, we believe it will be helpful for realizing quantum error-correction in the physical system.
