arXiv 2207.063972022-07-13quant-ph

张量训练交叉近似的量子态层析成像

Quantum state tomography with tensor train cross approximation

Alexander Lidiak, Casey Jameson, Zhen Qin, Gongguo Tang, Michael B. Wakin, Zhihui Zhu, Zhexuan Gong

备注：: 8 pages, 6 figures

摘要：

最近已经表明，由一维噪声量子计算机产生的状态可以很好地近似为具有与量子比特数量无关的有限键维数的矩阵乘积算子。我们表明，完整的量子态层析成像可以进行这样的状态与最小数量的测量设置使用一种方法称为张量训练交叉近似。该方法适用于重构满秩密度矩阵，并且仅需要测量局部算子，这在最先进的实验量子平台中常规地执行。我们的方法需要指数更少的状态副本比最知名的层析成像方法的非结构化状态和本地测量。我们重建状态的保真度可以通过监督机器学习进一步提高，而不需要更多的实验数据。如果可以从局部减少重建完整状态，则实现可缩放的层析成像。

英文摘要：

It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings using a method known as tensor train cross approximation. The method works for reconstructing full rank density matrices and only requires measuring local operators, which are routinely performed in state-of-art experimental quantum platforms. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements. The fidelity of our reconstructed state can be further improved via supervised machine learning, without demanding more experimental data. Scalable tomography is achieved if the full state can be reconstructed from local reductions.

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