Quantum state tomography with tensor train cross approximation
- URL: http://arxiv.org/abs/2207.06397v1
- Date: Wed, 13 Jul 2022 17:56:28 GMT
- Title: Quantum state tomography with tensor train cross approximation
- Authors: Alexander Lidiak, Casey Jameson, Zhen Qin, Gongguo Tang, Michael B.
Wakin, Zhihui Zhu, Zhexuan Gong
- Abstract summary: We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings.
Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
- Score: 84.59270977313619
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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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