We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional lattice, using physical quantum processors.
@article{arxiv.1911.11117,
title = {Quantum algorithms for disordered physics},
author = {Andrei Alexandru and Paulo F. Bedaque and Scott Lawrence},
journal= {arXiv preprint arXiv:1911.11117},
year = {2020}
}