**(ScientificAmerican)** Rolando Somma conducts research on quantum information theory and condensed matter physics in the Physics of Condensed Matter and Complex Systems Group of the Theoretical Division at Los Alamos National Laboratory. In this essay, Dr. Sommo asks, “When reliable, large-scale, error-tolerant quantum computers that can solve a wide range of useful problems, what should we do with them?” He explains that quantun ardware hasn’t caught up with theory, but we’re already lining up many previously intractable problems for when it does.

Feynman launched the field of quantum computing when he suggested that the best way to study quantum systems was to simulate them on quantum computers. Simulating quantum physics is the app for quantum computers.

In chemistry and nanoscale research, where quantum effects dominate, we could investigate the basic properties of materials and design new ones to understand mechanisms such as unconventional superconductivity. We could simulate and understand new chemical reactions and new compounds, which could aid in drug discovery.

By diving deep into mathematics and information theory, we already have developed many theoretical tools and the algorithms are farther along than the technology to build the actual machines.

Sommo and his colleagues have demonstrated very efficient algorithms to perform useful computations and study physical systems. We have also demonstrated one of the methods in one of the first small-scale quantum simulations ever done of a system of electrons, in a nuclear magnetic resonance quantum information processor.

Sommo closes by explaining that many of he and his colleagues are also taking a longer view, pushing theory deep into the intersection of quantum physics, information theory, complexity and mathematics and opening up new frontiers to explore, once we have the quantum computers to take us there.