A key requirement for an effective quantum error correction (QEC) scheme is that the physical qubits have error rates below a certain threshold. The value of this threshold depends on the details of the specific QEC scheme, and its hardware-level implementation. This is especially important with parity-check circuits, which are the fundamental building blocks of QEC codes. The standard way of constructing the parity check circuit is using a universal set of gates, namely sequential CNOT gates, single-qubit rotations and measurements. We exploit the insight that a QEC code does not require universal logic gates, but can be simplified to perform the sole task of error detection and correction. By building gates that are fundamental to QEC, we can boost the threshold and ease the experimental demands on the physical hardware. We present a rigorous formalism for constructing and verifying the error behavior of these gates, linking the physical measurement of a process matrix to the abstract error models commonly used in QEC analysis. This allows experimentalists to directly map the gates used in their systems to thresholds derived for a broad-class of QEC codes. We give an example of these new constructions using the model system of two nuclear spins, coupled to an electron spin, showing the potential benefits of redesigning fundamental gate sets using QEC primitives, rather than traditional gate sets reliant on simple single and two-qubit gates.

中文翻译：

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用于量子纠错的单步奇偶校验门组


有效的量子纠错（QEC）方案的一个关键要求是物理量子位的错误率低于特定阈值。该阈值的值取决于特定 QEC 方案的细节及其硬件级实现。这对于奇偶校验电路尤其重要，奇偶校验电路是 QEC 代码的基本构建块。构建奇偶校验电路的标准方法是使用一组通用门，即顺序 CNOT 门、单量子位旋转和测量。我们利用这样的见解：QEC 代码不需要通用逻辑门，但可以简化以执行错误检测和纠正的唯一任务。通过构建 QEC 的基础门，我们可以提高门槛并缓解对物理硬件的实验要求。我们提出了一种严格的形式来构建和验证这些门的错误行为，将过程矩阵的物理测量与 QEC 分析中常用的抽象错误模型联系起来。这使得实验人员可以将其系统中使用的门直接映射到为广泛的 QEC 代码派生的阈值。我们使用两个核自旋与一个电子自旋耦合的模型系统给出了这些新结构的示例，展示了使用 QEC 原语重新设计基本门集的潜在好处，而不是依赖于简单的单量子位门和两个量子位门的传统门集。