Electronic Band Structure of Silicon Determined via a Variational Adiabatic Eigensolver: Theory and Experiment

• URL: http://arxiv.org/abs/2606.16604v1
• Date: Mon, 15 Jun 2026 11:51:16 GMT
• Title: Electronic Band Structure of Silicon Determined via a Variational Adiabatic Eigensolver: Theory and Experiment
• Abstract summary: We introduce adiabatic eigensolver protocol to prepare high-fidelity eigenstates on noisy quantum devices.<n>We successfully compute the electronic band structure of silicon using only a modest number of qubits.<n>This framework provides a robust and practical pathway for precisely determining electronic structures in quantum materials.
• Score: 13.777428345019553
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work addresses the critical challenge of excited-state preparation for semiconductor band structure calculations. We introduce a variational adiabatic eigensolver (VAE) protocol that combines adiabatic evolution with variational optimization to prepare high-fidelity eigenstates on noisy intermediate-scale quantum (NISQ) devices. Applying a momentum-space truncation, we accurately compute the electronic band structure of silicon -- an idealized infinite periodic system -- using only a modest number of qubits. Our approach employs multi-qubit parameterized circuits and a phase-based loss function, overcoming limitations of conventional methods. These limitations include the circuit-construction difficulty in traditional adiabatic approaches and the reduced accuracy of variational quantum eigensolvers for excited states. Through rigorous numerical simulation and experimental implementation on a superconducting quantum processor, we successfully prepare silicon's valence-band and conduction-band eigenstates. Single-shot readout yields state fidelities exceeding 96%, and the measured energy expectations agree with theoretical band energies within 0.5 eV. Further refinement via single-frequency oscillation fitting reduces the energy deviation to below 0.01 eV. This framework provides a robust and practical pathway for precisely determining electronic structures in quantum materials.

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