Quantum computers vs. differential equations: IBM video shows potential and limits

IBM released a new episode of its podcast and video series “The Coherence Times” on 13 October, which is also available on the IBM Research YouTube channel. Host Ryan Mandelbaum talks with Hari Krovi, senior research staff member and manager at IBM, and Di Fang, assistant professor of mathematics at Duke University, about quantum algorithms for differential equations. Such equations describe how systems change over time – from electrical circuits to fluid flows and plasma physics – and often demand enormous computing power.

In an interview on the IBM Research blog, Krovi explained that when simulating RLC circuits, the runtime of the quantum approach grows only logarithmically with the number of components, whereas classical simulations typically scale linearly; so far this applies only to linear components. According to him, the Navier-Stokes equations for fluid flow can be solved on quantum computers only in mild, laminar regimes – highly turbulent flows remain out of reach for now.

Krovi names loading data into the quantum computer and extracting classical results as the biggest hurdles. The episode also covers the challenges real quantum hardware still poses and what is needed for quantum computers to make a real impact in science and engineering.