arXiv 2003.071252020-03quant-ph

局域费米编码中的误差消除

Mitigating Errors in Local Fermionic Encodings

Johannes Bausch, Toby Cubitt, Charles Derby, Joel Klassen

备注：: 21 pages; v2: minor changes to intro and references

摘要：

费米子多体系统的量子模拟主要依赖于从不可区分的费米子到可区分的量子比特的映射。费米子Fock空间的非定域结构需要将局部费米子算子映射到非局部量子比特算子的编码，或者将费米子表示编码在长程纠缠码空间中。在后一种情况下，在编码的两个理想属性之间存在不可避免的权衡：局部费米子算子的低权重表示和高距离代码空间。在这里，有人认为，尽管有这个基本的限制，费米编码与低权重表示的本地费米算子仍然可以表现出错误缓解性能，可以起到类似的作用，由高代码距离。特别是当不可检测的错误对应于“自然”的费米噪声。我们说明这一点明确的两个费米子编码：Verstraete-Cirac编码，和编码出现在并行工作的德比和克拉森。在这些编码中，可以检测到许多但不是全部的单量子比特错误。然而，我们发现，剩余的不可检测的单量子比特错误映射到本地，低权重的费米子相位噪声。我们认为，这样的噪音是自然的费米晶格模型。这表明，即使采用低权重的费米编码，错误率也可以以类似于高距离码的方式被抑制，只要人们愿意在他们的模拟费米系统中接受模拟的自然费米噪声。

英文摘要：

Quantum simulations of fermionic many-body systems crucially rely on mappings from indistinguishable fermions to distinguishable qubits. The non-local structure of fermionic Fock space necessitates encodings that either map local fermionic operators to non-local qubit operators, or encode the fermionic representation in a long-range entangled code space. In this latter case, there is an unavoidable trade-off between two desirable properties of the encoding: low weight representations of local fermionic operators, and a high distance code space. Here it is argued that despite this fundamental limitation, fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties which can serve a similar role to that played by high code distances. In particular when undetectable errors correspond to "natural" fermionic noise. We illustrate this point explicitly for two fermionic encodings: the Verstraete-Cirac encoding, and an encoding appearing in concurrent work by Derby and Klassen. In these encodings many, but not all, single-qubit errors can be detected. However we show that the remaining undetectable single-qubit errors map to local, low-weight fermionic phase noise. We argue that such noise is natural for fermionic lattice models. This suggests that even when employing low-weight fermionic encodings, error rates can be suppressed in a similar fashion to high distance codes, provided one is willing to accept simulated natural fermionic noise in their simulated fermionic system.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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