Revisiting semiconductor bulk hamiltonians using quantum computers

TL;DR

This paper demonstrates how quantum computers can simulate the electronic properties of III-V semiconductors using variational methods and Hamiltonian descriptions, achieving accurate band structures and transition probabilities.

Contribution

It introduces a quantum computational approach to model semiconductor Hamiltonians and validates it with various simulators, including real noisy quantum devices.

Findings

Quantum simulations produce band structures in good agreement with classical methods.

Simulation times vary based on optimizer, circuit depth, and simulator.

Quantum eigenstates enable analysis of inter-band absorption probabilities.

Abstract

With the advent of near-term quantum computers, the simulation of properties of solids using quantum algorithms becomes possible. By an adequate description of the system's Hamiltonian, variational methods enable to fetch the band structure and other fundamental properties as transition probabilities. Here, we use k$\cdot$p Hamiltonians to describe semiconductor structures of the III-V family and obtain their band structures using a state vector solver, a probabilistic simulator, and a real noisy-device simulator. The resulting band structures are in good agreement with the ones obtained by direct diagonalization of the Hamiltonian. Simulation times depend on the optimizer, circuit depth, and simulator used. Finally, with the optimized eigenstates, we convey the inter-band absorption probability, demonstrating the possibility of analyzing the fundamental properties of crystalline systems using quantum computers.