Diagonalization of large many-body Hamiltonians on a quantum processor

TL;DR

This paper demonstrates the use of a superconducting quantum processor to perform quantum diagonalization of large many-body Hamiltonians, enabling eigenenergy estimation for systems with up to 56 sites, which could complement classical methods.

Contribution

It introduces a quantum diagonalization approach using the Krylov algorithm on a superconducting processor for large-scale many-body systems.

Findings

Successfully computed eigenenergies of 2D lattice systems with up to 56 sites.

Implemented Trotterized unitaries to construct subspaces for diagonalization.

Quantum diagonalization can complement classical methods in quantum physics.

Abstract

The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments show that quantum diagonalization algorithms are poised to complement their classical counterpart at the foundation of computational methods for quantum systems.