论文标题
量子错误检测无需使用Ancilla Qubit
Quantum Error Detection Without Using Ancilla Qubits
论文作者
论文摘要
在本文中，我们描述并在实验上证明了不使用Ancilla Qubits或中路测量的错误检测方案。这是通过扩展Hilbert空间来实现的，其中使用几个物理量子位编码单个逻辑量子位。例如，一个可能的两个量子编码标识$ | 0 \ rangle_l = | 01 \ rangle $和$ | 1 \ rangle_l = | 10 \ rangle $。如果在最终测量中观察到$ | 11 \ rangle $或$ | 00 \ rangle $，则声明了错误，并且该运行未包括在后续分析中。我们提供用于简单的位叉编码的代码字，一种编码状态的方法，一种实现逻辑$ u_3 $和逻辑$ C_X $门的方法，以及可以检测到哪些错误的描述。然后，我们在基于Transmon的IBM量子计算机上运行Greenberger-Horne-Zeilinger电路，其输入空间为$ n \ in \ {2,3,4,5 \} $逻辑Qubits和$ q \ in \ in \ {1,2,3,4,5 \ \} $物理Qubits Qubits。将结果相对于$ q = 1 $在\ {2,3,4 \} $中的$ q \中进行了显着改善。
In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded using several physical qubits. For example, one possible two qubit encoding identifies $|0\rangle_L=|01\rangle$ and $|1\rangle_L=|10\rangle$. If during the final measurement a $|11\rangle$ or $|00\rangle$ is observed an error is declared and the run is not included in subsequent analysis. We provide codewords for a simple bit-flip encoding, a way to encode the states, a way to implement logical $U_3$ and logical $C_x$ gates, and a description of which errors can be detected. We then run Greenberger-Horne-Zeilinger circuits on the transmon based IBM quantum computers, with an input space of $N\in\{2,3,4,5\}$ logical qubits and $Q\in\{1,2,3,4,5\}$ physical qubits per logical qubit. The results are compared relative to $Q=1$ with and without error detection and we find a significant improvement for $Q\in\{2,3,4\}$.
