Regensburg 2022 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 3: Certification and Benchmarking of Quantum Systems
QI 3.2: Vortrag
Montag, 5. September 2022, 15:30–15:45, H8
Compressive gate set tomography — •Raphael Brieger1, Ingo Roth2, and Martin Kliesch1 — 1Quantum technology, Heinrich Heine University Düsseldorf, Germany — 2Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
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. 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 and is therefore more broadly applicable than traditional approaches.