TY  - JOUR
AU  - Funcke, Lena
AU  - Hartung, Tobias
AU  - Jansen, Karl
AU  - Kühn, Stefan
AU  - Stornati, Paolo
TI  - Dimensional Expressivity Analysis of Parametric Quantum Circuits
JO  - Quantum
VL  - 5
IS  - arXiv:2011.03532
SN  - 2521-327X
CY  - Wien
PB  - Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
M1  - PUBDB-2021-02288
M1  - arXiv:2011.03532
M1  - HU-EP-20/31
SP  - 422 -
PY  - 2021
N1  - Quantum 5, 422 (2021). 37 pages, 13 figures, journal version
AB  - Parametric 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.
KW  - hardware (INSPIRE)
KW  - parametric (INSPIRE)
KW  - hybrid (INSPIRE)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000636649700001
DO  - DOI:10.22331/q-2021-03-29-422
UR  - https://bib-pubdb1.desy.de/record/458706
ER  -