Limitations of quantum computing with Gaussian cluster states
Limitations of quantum computing with Gaussian cluster states
复制标题
高斯簇态量子计算的局限性
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
J. Eisert
中科院分区：
文献类型：
--
作者：
M. Ohliger;K. Kieling;J. Eisert
我们讨论高斯簇状态对于基于测量的量子计算的潜力和局限性。使用高斯投影纠缠对态框架，我们表明，无论对分布在一般图上的系统执行什么高斯局部测量，除了指数抑制校正之外，量子信息的传输和处理都不可能超出某个影响区域。我们还证明，即使在任意非高斯局部测量下，有限宽度的高斯簇状态板也无法携带逻辑量子信息，即使允许连续变量系统中的量子位进行复杂的编码。这可以通过适当收缩代表无限维量子系统的张量网络来证明。结果可以看作是提高了对高斯簇状态的量子纠错和容错的要求，并指出了基于测量的量子计算非高斯资源状态的必要性。结果同样可以被视为参考高斯量子中继器网络。
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian-projected entangled pair states, we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information are not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states and points toward the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.