Solving a 16-Year Old Problem in Quantum Computation: The Postelection-Improved HHL Framework.
Linear equations are used to model systems across almost all areas of science and engineering. Solving these linear systems allows us to gain a better understanding of the system, its properties, as well as how it reacts under different situations (simulations).
One of the most well-known quantum algorithms to numerically solve linear systems is the Harrow-Hassidim-Lloyd (HHL) algorithm. The HHL algorithm provides results exponentially quicker than classical counterparts. But it becomes unreliable for systems with a large ‘condition number’ (𝜅)—a problem that has persisted for 16 years.
Recently, a team, including reseachers from CQuERE, TCG CREST, has put forth a novel postselection-improved HHL (Psi, Ψ-HHL) that can address the runtime issue for systems with a large κ without involving extra quantum resources. The researchers also demonstrated the performance of the new algorithm by carrying out numerical simulations up to 26-qubit calculations for large κ systems.
The novel algorithm could find applications in quantum chemistry, to calculate the properties of large molecules, and in many other fields where linear systems are prevalent.
Read the full paper in the Physical Review Research , here.