A systematic variational approach to band theory in a quantum computer

Area of Science:

• Quantum Computing
• Materials Science
• Computational Chemistry

Background:

• Quantum computing offers potential for molecular simulation, with algorithms like Quantum Phase Estimation and Variational Quantum Eigensolver under development.
• Current quantum hardware limitations (qubit count, fidelity) hinder complex applications, particularly in crystalline phases requiring compact orbital bases.

Purpose of the Study:

• To develop a hybrid quantum-classical algorithm for calculating the band structure of periodic systems using tight-binding models.
• To assess the algorithm's performance on quantum simulators with noise and on actual IBM quantum hardware.

Main Methods:

• A hybrid quantum-classical algorithm was designed for band structure calculations.
• The algorithm was tested on a simple-cubic crystal model (polonium) using quantum simulators and IBM quantum computers.
• Performance was evaluated under varying noise conditions and computational complexity was analyzed.

Main Results:

• The algorithm proved reliable on low-noise devices and functional, albeit with low precision, on current noisy quantum computers.
• The computational complexity scales as Ω(M^3) with the number of orbitals (M), comparable to classical methods.
• Simulations provided insights into optimizing quantum algorithms for specific tasks like band structure calculations.

Conclusions:

• The developed hybrid algorithm is a viable approach for band structure calculations on near-term quantum devices.
• The study highlights the potential of quantum computing for materials science and condensed matter physics.
• Optimization of quantum algorithms for specialized problems like band structure calculations is feasible and beneficial.