Quantum linear algebra for disordered electrons

TL;DR

This paper presents a quantum linear algebra framework for simulating disordered non-interacting electrons, enabling efficient computation of physical properties that are challenging for classical methods, especially in higher dimensions.

Contribution

It introduces a quantum algorithmic approach for simulating disordered electron systems using block-encoding and quantum singular value transformation, highlighting potential quantum advantages.

Findings

Quantum algorithms can simulate key physical quantities of disordered electrons.

Quantum advantage scales polynomially with system size and exponentially with lattice dimension.

The approach overcomes limitations of classical disorder-averaged methods.

Abstract

We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons. The physics of disordered electrons outside of one dimension challenges classical computation due to the critical nature of the Anderson localization transition or the presence of large localization lengths, while the atypical distribution of the local density of states limits the power of disorder averaged approaches. Starting from the block-encoding of a disordered non-interacting Hamiltonian, we describe how to simulate key physical quantities, including the reduced density matrix, Green's function, and local density of states, as well as bulk-averaged observables such as the linear conductivity, using the quantum singular value transformation, quantum amplitude estimation, and trace estimation. We further discuss a quantum advantage that scales polynomially with system size and exponentially with lattice dimension.