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IQIM Postdoctoral and Graduate Student Seminar

Wednesday, February 23, 2022
11:00am to 12:00pm
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Compressive gate set tomography
Martin Kliesch, University of Düsseldorf,

Joint IQIM/AWS Seminar

Abstract: Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomography a challenging task even for only two qubits.

In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them randomly. Such tomographic information is needed for the crucial task of dealing with coherent noise. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics by using second-order geometrical optimization methods on the complex Stiefel manifold. Besides the reduction in sequences, we demonstrate numerically that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography. Therefore, it is arguably more flexible than traditional approaches.

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