Full Band Structure Calculation of Semiconducting Materials on a Noisy
  Quantum Processor
Quantum chemistry is a promising application in the era of quantum computing
since the unique effects of quantum mechanics that take exponential growing
resources to simulate classically are controllable on quantum computers.
Fermionic degrees of freedom can be encoded efficiently onto qubits and allow
for algorithms such as the Quantum Equation-of-Motion method to find the entire
energy spectrum of a quantum system. In this paper, we propose the Reduced
Quantum Equation-of-Motion method by reducing the dimensionality of its
generalized eigenvalue equation, which results in half the measurements
required compared to the Quantum Equation-of-Motion method, leading to speed up
the algorithm and less noise accumulation on real devices. In particular, we
analyse the performance of our method on two noise models and calculate the
excitation energies of a bulk Silicon and Gallium Arsenide using our method on
an IBM quantum processor. Our method is fully robust to the uniform
depolarizing error and we demonstrate that the selection of suitable atomic
orbital complexity could increase the robustness of our algorithm under real
noise. We also find that taking the average of multiple experiments tends
towards the correct energies due to the fluctuations around the exact values.
Such noise resilience of our approach could be used on current quantum devices
to solve quantum chemistry problems.
Shaobo Zhang Akib Karim Harry M. Quiney Muhammad Usman