Polynomial-time classical and quantum simulation of quantum impurity models
What quantum computers can and cannot do faster than classical ones
Classical computers can efficiently calculate the static properties of quantum impurity models—a fundamental building block in materials science—contrary to what researchers previously thought possible. However, quantum computers have a genuine advantage when it comes to simulating how these systems evolve over time, suggesting a clear dividing line between what each type of machine does best.
Quantum impurity models underpin how scientists predict the behavior of real materials and design new ones. Knowing that classical computers can handle the most common calculations—ground-state energies and thermal properties—means researchers can solve many practical problems without quantum hardware. But the finding that quantum computers excel at time-dependent simulations identifies where quantum machines will deliver real value, helping guide which quantum computers get built first and which problems are worth solving with them.