论文标题
通过平衡重量-2 $ z $ stabilizers来缓解连贯的噪音
Mitigating Coherent Noise by Balancing Weight-2 $Z$-Stabilizers
论文作者
论文摘要
物理平台（如被困离子）遭受连贯的噪声，其中错误表现为围绕特定轴的旋转，并且可以随着时间的推移积累。我们通过无抗性子空间调查被动缓解，要求噪声保留稳定器代码的代码空间，并充当受保护信息的逻辑身份操作员。因此，我们为所有横向$ z $ rotations开发了必要的条件，以保留稳定器代码的代码空间，这些代码空间需要 - $ 2 $ $ z $ stabilizers来覆盖所有用于支持一些$ x $ component的量子。此外，重量-2 $ $ $ z $ -Stabilizers生成了具有均匀块长度的单位检查代码的直接产品。通过调整这些组件的大小，我们能够构建一个QECC代码的大型QECC代码，即一致的噪声，其中包括$ [4L^2，1，2L]] $ shor代码。此外，给定$ m $偶数和任何$ [[n，k，d]] $稳定器代码，我们可以构建一个$ [Mn，K，\ ge d]] $稳定器代码，该代码遗忘了连贯的噪声。 如果我们要求横向$ z $ - 旋转将代码空间保留到Clifford层次结构中的某些有限级$ L $，那么我们可以构建通用量子计算所需的更高级别的门。每个非零$ x $ -Component支持的$ z $ stabilizers形成了经典的二进制代码C，该代码C必须包含一个自偶代码，而经典的Gleason定理则限制了其权重枚举器。稳定代码的条件由横向$2π/2^l $ $ $ z $ - 旋转$ 4 \ le l \ le l \ le l _ {\ max} <\ iftty $在克利福德层次结构中的级别，导致格里森（Gleason）Theorem的概括，可能对经典编码的理论家具有独立的兴趣。
Physical platforms such as trapped ions suffer from coherent noise where errors manifest as rotations about a particular axis and can accumulate over time. We investigate passive mitigation through decoherence free subspaces, requiring the noise to preserve the code space of a stabilizer code, and to act as the logical identity operator on the protected information. Thus, we develop necessary and sufficient conditions for all transversal $Z$-rotations to preserve the code space of a stabilizer code, which require the weight-$2$ $Z$-stabilizers to cover all the qubits that are in the support of some $X$-component. Further, the weight-$2$ $Z$-stabilizers generate a direct product of single-parity-check codes with even block length. By adjusting the size of these components, we are able to construct a large family of QECC codes, oblivious to coherent noise, that includes the $[[4L^2, 1, 2L]]$ Shor codes. Moreover, given $M$ even and any $[[n,k,d]]$ stabilizer code, we can construct an $[[Mn, k, \ge d]]$ stabilizer code that is oblivious to coherent noise. If we require that transversal $Z$-rotations preserve the code space only up to some finite level $l$ in the Clifford hierarchy, then we can construct higher level gates necessary for universal quantum computation. The $Z$-stabilizers supported on each non-zero $X$-component form a classical binary code C, which is required to contain a self-dual code, and the classical Gleason's theorem constrains its weight enumerator. The conditions for a stabilizer code being preserved by transversal $2π/2^l$ $Z$-rotations at $4 \le l \le l_{\max} <\infty$ level in the Clifford hierarchy lead to generalizations of Gleason's theorem that may be of independent interest to classical coding theorists.
