IBM's Heron R3 quantum computer handled a task that made a classical method back down. The challenge was finding the ground state, the lowest energy level, of a system of 49 quantum bits.
The classical method SCI (selected configuration interaction) tries out configurations, but on this problem it failed to find the correct answer. The quantum algorithm, based on sampling and Krylov diagonalization, succeeded. It didn't need to solve the full Schrödinger equation — instead, it built the approximation step by step, like a person finding their way through fog, taking short steps and checking the direction.
Classical iterative solvers tuned specifically to this construction might still find a solution. But standard SCI cannot. This is the first time a quantum algorithm on real hardware has outperformed a classical one for a ground-state energy problem.
This experiment not only shows the advantage of quantum computing but also offers hope for solving real problems in chemistry, where accurate calculation of molecular energies is key to new materials and drugs.
49 qubits can be in a state described by a vector in a space of dimension $2^{49}$—a number larger than the number of atoms in the visible universe.
In Greg Egan's story "The Quantum Thief," quantum computers crack any encryption using similar search algorithms.