Variational Quantum Algorithms (VQAs) provide a promising framework for solving electronic structure problems using the computational capabilities of quantum computers to explore high-dimensional Hilbert spaces efficiently. This research investigates the performance of VQAs in electronic structure calculations of gallium arsenide (GaAs), a semiconductor with a zinc-blende structure. Utilizing a tight-binding Hamiltonian and a Jordan-Wigner-like transformation, we map the problem to a 10-qubit Hamiltonian. We analyze the impact of quantum circuit architectures, algorithm hyperparameters, and optimization methods on two VQAs: Variational Quantum Deflation (VQD) and Subspace Search Variational Quantum Eigensolver (SSVQE). We observed that while both algorithms offer promising results, the choice of ansatz and hyperparameter tuning were especially critical in achieving reliable outcomes, particularly for higher energy states. Adjusting the hyperparameters in VQD significantly enhanced the accuracy of higher energy state calculations, reducing the error by an order of magnitude, whereas tuning the hyperparameters in SSVQE had minimal impact. Our findings provide insights into optimizing VQAs for electronic structure problems, paving the way for their application to more complex systems on near-term quantum devices.

Department of Condensed Matter Physics Faculty of Science Masaryk University 611 37 Brno Czech Republic

Institute of Physics of Materials Czech Academy of Sciences 616 00 Brno Czech Republic

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Cao, Y. et al. Quantum chemistry in the age of quantum computing. PubMed DOI

Bauer, B., Bravyi, S., Motta, M. & Chan, G.K.-L. Quantum algorithms for quantum chemistry and quantum materials science. PubMed DOI

de Leon, N. P. et al. Materials challenges and opportunities for quantum computing hardware. PubMed DOI

Stanisic, S. et al. Observing ground-state properties of the fermi-hubbard model using a scalable algorithm on a quantum computer. PubMed DOI PMC

Wecker, D., Hastings, M. B. & Troyer, M. Progress towards practical quantum variational algorithms. DOI

Lischka, H. et al. Multireference approaches for excited states of molecules. PubMed DOI

Schuch, N. & Verstraete, F. Computational complexity of interacting electrons and fundamental limitations of density functional theory. DOI

Burke, K. Perspective on density functional theory. PubMed DOI

Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. PubMed DOI

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. PubMed DOI PMC

Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. PubMed DOI

Higgott, O., Wang, D. & Brierley, S. Variational quantum computation of excited states. DOI

Nakanishi, K. M., Mitarai, K. & Fujii, K. Subspace-search variational quantum eigensolver for excited states. DOI

Sherbert, K., Cerasoli, F. & Buongiorno Nardelli, M. A systematic variational approach to band theory in a quantum computer. PubMed DOI PMC

Vogl, P., Hjalmarson, H. P. & Dow, J. D. A semi-empirical tight-binding theory of the electronic structure of semiconductors. DOI

Barkoutsos, P. K. et al. Quantum algorithms for electronic structure calculations: Particle-hole hamiltonian and optimized wave-function expansions. DOI

Gard, B. T. et al. Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm. DOI

Uvarov, A. V., Kardashin, A. S. & Biamonte, J. D. Machine learning phase transitions with a quantum processor. DOI

Qiskit: An open-source framework for quantum computing. https://www.ibm.com/quantum/qiskit/ Accessed on 18 May 2024 (2024).

Bierman, J. Ssvqe. https://github.com/JoelHBierman/SSVQE/ Accessed on 18 May 2024 (2024).

Ďuriška, M., Miháliková, I. & Friák, M. Quantum computing of the electronic structure of crystals by the variational quantum deflation algorithm. DOI

Carlo, A. D. Microscopic theory of nanostructured semiconductor devices: beyond the envelope-function approximation. DOI