Quantum error-detection at low energies
Quantum error-detection at low energies
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DOI：
10.1007/jhep09(2019)021
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发表时间：
2019-02
影响因子：
5.4
通讯作者：
Martina Gschwendtner;Robert Koenig;B. Sahinoglu;Eugene Tang
中科院分区：
文献类型：
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作者：
Martina Gschwendtner;Robert Koenig;B. Sahinoglu;Eugene Tang
基于量子纠错、拓扑序、全息AdS/CFT对偶性和张量网络之间的密切关系，我们研究了矩阵乘积态（MPS）中的近似量子检错码.我们首先表明，使用开放边界MPS定义边界批量编码映射产生最恒定的距离检错码。这些是有缺口的局部哈密顿的退化的地面空间。为了解决这个不可行的结果，我们考虑激发态，即，我们使用激发假设来构造编码映射：对于任何v ∈（0，1）和Ω（log n）编码的量子比特，这些生成距离为Ω（n1-v）的错误检测码。这表明，有隙系统包含在孤立的能带误差检测码跨越动量本征态。我们还考虑了无带隙的海森堡-XXX模型，其能量本征态可以通过Bethe张量网络来描述。我们发现，它包含在其低能量特征空间内的错误检测码具有相同的参数缩放。所有这些代码检测任意d-本地（不一定是几何本地）错误，即使他们不是置换不变。这表明，大范围的自然发生的多体系统具有内在的错误检测功能。
Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states (MPS). We first show that using open-boundary MPS to define boundary to bulk encoding maps yields at most constant distance error-detecting codes. These are degenerate ground spaces of gapped local Hamiltonians. To get around this no-go result, we consider excited states, ie, we use the excitation ansatz to construct encoding maps: these yield error-detecting codes with distance Ω (n 1− ν) for any ν∈(0, 1) and Ω (log n) encoded qubits. This shows that gapped systems contain—within isolated energy bands—error-detecting codes spanned by momentum eigenstates. We also consider the gapless Heisenberg-XXX model, whose energy eigenstates can be described via Bethe ansatz tensor networks. We show that it contains—within its low-energy eigenspace—an error-detecting code with the same parameter scaling. All these codes detect arbitrary d-local (not necessarily geometrically local) errors even though they are not permutation-invariant. This suggests that a wide range of naturally occurring many-body systems possess intrinsic error-detecting features.