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000458706 245__ $$aDimensional Expressivity Analysis of Parametric Quantum Circuits
000458706 260__ $$aWien$$bVerein zur Förderung des Open Access Publizierens in den Quantenwissenschaften$$c2021
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000458706 500__ $$aQuantum 5, 422 (2021). 37 pages, 13 figures, journal version
000458706 520__ $$aParametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, we develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.
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000458706 7001_ $$0P:(DE-HGF)0$$aHartung, Tobias$$b1
000458706 7001_ $$0P:(DE-H253)PIP1003636$$aJansen, Karl$$b2$$udesy
000458706 7001_ $$0P:(DE-HGF)0$$aKühn, Stefan$$b3
000458706 7001_ $$0P:(DE-H253)PIP1083971$$aStornati, Paolo$$b4$$udesy
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