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, 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.
 F. G. S. L. Brandao and K. M. Svore. Quantum speed-ups for solving semidefinite programs. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pages 415–426, 2017.
 M. Troyer and U.-J. Wiese. Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations. Phys. Rev. Lett., 94: 170201, 2005.
 K. Temme, S. Bravyi, and J. M. Gambetta. Error mitigation for short-depth quantum circuits. Phys. Rev. Lett., 119: 180509, 2017.
 A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549: 242, 2017.
 K. Yeter-Aydeniz, R. C. Pooser, and G. Siopsis. Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and lanczos algorithms. npj Quantum Information, 6: 63, 2020.
 L. Funcke, T. Hartung, K. Jansen, S. Kühn, P. Stornati, and X. Wang. Measurement error mitigation in quantum computers through classical bit-flip correction. arXiv:2007.03663, 2020.
 A. Peruzzo, J. McClean, P. Shadbolt, M. Yung, X. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun., 5: 1, 2014.
 J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New J. Phys., 18: 023023, 2016.
 D. Paulson, L. Dellantonio, J. F. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, and C. A. Muschik. Towards simulating 2d effects in lattice gauge theories on a quantum computer. arXiv:2008.09252, 2020.
 J. F. Haase, L. Dellantonio, A. Celi, D. Paulson, A. Kan, K. Jansen, and C. A. Muschik. A resource efficient approach for quantum and classical simulations of gauge theories in particle physics. Quantum, 5: 393, 2021.
 M. R. Geller. Sampling and scrambling on a chain of superconducting qubits. Physical Review Applied, 10: 024052, 2018.
 S. Sim, P. D. Johnson, and A. Aspuru‐Guzik. Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum‐classical algorithms. Adv. Quantum Technol., 2: 1900070, 2019.
 S. Sim, J. Romero, J. F. Gonthier, and A. A. Kunitsa. Adaptive pruning-based optimization of parameterized quantum circuits. Quantum Sci. Technol., 6: 025019, 2020.
 S. E. Rasmussen, N. J. S. Loft, T. Bækkegaard, M. Kues, and N. T. Zinner. Reducing the amount of single‐qubit rotations in vqe and related algorithms. Adv. Quantum Technol., 3: 2000063, 2020.
 T. Hubregtsen, J. Pichlmeier, P. Stecher, and K. Bertels. Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility and entangling capability. arXiv:2003.09887, 2020.
 B. T. Gard, L. Zhu, G. S. Barron, N. J. Mayhall, S. E. Economou, and E. Barnes. Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm. npj Quantum Information, 6: 10, 2020.
 G. S. Barron, B. T. Gard, O. J. Altman, N. J. Mayhall, E. Barnes, and S. E. Economou. Preserving symmetries for variational quantum eigensolvers in the presence of noise. arXiv:2003.00171, 2020.
 Qiskit documentation, 2020. https://qiskit.org/documentation/_modules/qiskit/circuit/library/n_local/efficient_su2.html. accessed on 2020/07/14.
 Tobias Haug, Kishor Bharti, and M. S. Kim, "Capacity and quantum geometry of parametrized quantum circuits", arXiv:2102.01659.
 Kamal Choudhary, "Quantum Computation for Predicting Solids-state Material Properties", arXiv:2102.11452.
 Tom Weber, Matthias Riebisch, Kerstin Borras, Karl Jansen, and Dirk Krücker, "Modelling for Quantum Error Mitigation", arXiv:2104.07320.
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