Quantum algorithms for chemistry and materials

4 problems

• Is there exponential quantum advantage for molecular ground-state energies?

  Contested

  Quantum computers are often said to be exponentially faster for chemistry, but classical methods keep improving. Whether there is a real exponential gap for a growing family of real molecules is disputed.

• Where classical methods stop for FeMoco-class iron-sulfur clusters

  Open

  The iron-molybdenum cluster in nitrogenase, the enzyme that turns nitrogen from air into ammonia, was long the flagship target for quantum chemistry on quantum computers. A 2026 classical calculation reached the target accuracy for the standard model, so it is open which larger or harder version still needs a quantum computer.

• Fault-tolerant cost to beat classical methods on the 2D Hubbard model

  Open

  The two-dimensional Hubbard model, a simple model of electrons hopping on a grid and repelling each other, is a likely first case where a quantum computer could outdo classical methods. How many error-corrected qubits and operations that would take is not pinned down.

• Scaling of ground-state overlap for classically preparable trial states

  Open

  Quantum phase estimation needs a starting state that resembles the true ground state. If the best starting states that ordinary computers can prepare become exponentially worse as molecules grow, the quantum speedup disappears.