Quantum algorithms for disordered physics

TL;DR

This paper introduces a quantum algorithm that efficiently simulates disordered quantum systems, such as Anderson localization, using minimal qubits and gates, and demonstrates its application on both simulated and physical quantum processors.

Contribution

It presents a novel quantum simulation method for disordered Hamiltonians that integrates pseudo-random number generation into the evolution circuit, enabling scalable simulations.

Findings

Successfully simulated Anderson localization and metal-insulator transition.

Achieved efficient resource scaling with system size.

Demonstrated practical implementation on physical quantum hardware.

Abstract

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.