Observation of Improved Accuracy over Classical Sparse Ground-State Solvers using a Quantum Computer

TL;DR

This paper demonstrates that a hybrid quantum-classical algorithm can outperform classical methods in finding ground states of certain sparse Hamiltonian problems, showcasing the potential of quantum algorithms for specific quantum chemistry tasks.

Contribution

It provides experimental evidence that a sample-based quantum diagonalization algorithm can outperform classical heuristics on a 49-qubit problem, addressing an open research question.

Findings

Quantum algorithm succeeded where classical heuristics failed

Quantum approach achieved better accuracy on a 49-qubit problem

Experimental validation on IBM hardware supports quantum advantage potential

Abstract

We experimentally demonstrate that a hybrid quantum-classical algorithm can outperform purely classical, off-the-shelf selected configuration interaction methods. First, we construct a class of local Hamiltonian problems with sparse ground states, and show that representative classical heuristics fail to find the ground state of a specific 49-qubit instance. Next, we show that the sample-based Krylov quantum diagonalization algorithm, run on an IBM Heron R3 processor, succeeds at the same task. This algorithm uses quantum samples from a grid of time-evolved quantum states, and offers provable convergence guarantees for sparse ground state problems with guiding states. While the problem is also solvable classically using two iterative solvers that we designed specifically to target our Hamiltonian construction, this work resolves the previously open question of whether a sample-based quantum diagonalization algorithm can outperform standard selected configuration interaction heuristics.