Seminar"Effects of gate errors in digital quantum simulations of fermionic systems"

Title: "Effects of gate errors in digital quantum simulations of fermionic systems"

Speaker: Prof. Gerd Schön, Karlsruhe Institute of Technology, Germany

Abstract:

Today several companies (Google, IBM, Rigetti, ...) are building quantum computers based on superconducting Josephson junction quantum bits. They offer exciting perspectives to perform digital quantum simulations of quantum mechanical systems such as molecules or fermionic lattice models. Once these computers have a sufficient size and quality they will outperform all classical computers. The most serious problem are errors due to the influence of the environment or the control of the gates. In principle quantum error correction could provide a remedy. However, it would require very large systems, out of reach for present-day technology. It is therefore important to study the use of small size quantum computers with non-vanishing error rates.

We study the influence of gate errors on simulations of the time evolution of the quantum system based on the Trotter expansion. Specifically we consider the effect of stochastic over-rotations in the applied gates with focus on the fermionic Hubbard model. We establish the relation between the gate fidelity and the strength of the over-rotations. Depending on the particular algorithm implemented such gate errors lead to a time evolution that corresponds to a disordered fermionic system. For different algorithms the errors may correspond to unphysical errors, e.g., they can violate particle number conservation. We also study the effect of gate errors when using the variational Hamiltonian ansatz to find the ground state of the Fermi-Hubbard model.

We substantiate our analysis by numerical simulations of model systems.

The talk is based on the papers

J.-M. Reiner, S. Zanker, I. Schwenk, J. Leppäkangas, F. Wilhelm-Mauch, G. Schön, and M. Marthaler, Quantum Science and Technology 3, 045008 (2018)

J.M. Reiner, F.K. Wilhelm, G. Schön and M. Marthaler, arXiv:1811.04476