The “nightmare” calculations would be too difficult even for quantum computers

Researchers have identified a “nightmare scenario” calculation involving exotic types of quantum matter that would be impossible to solve, even for a highly efficient quantum computer.

Without the complexity of quantum states of matter, determining the phase of matter can be relatively simple. Take water for example, it is easy to know whether it is in a solid or liquid state. However, the quantum version of this task could be more difficult. Thomas Schuster Now his colleagues at Caltech have demonstrated that determining quantum phases of matter can be extremely difficult even for quantum computers.

They have mathematically analyzed a scenario in which a set of measurements about the quantum state of an object is fed to a quantum computer and it has to determine its phase. Schuster says this isn’t always an impossible problem, but his team has shown that for much of the quantum phases of matter — the more exotic relatives of liquid water and ice, such as “topological” phases characterized by strange electric currents — a quantum computer would need to perform calculations for an impossibly long time. The situation is like the worst version of laboratory experiments, where determining sample properties requires keeping the instrument running for billions or trillions of years.

This does not make quantum computers practically obsolete for this task. Schuster says these phases are unlikely to appear in actual experiments with materials or quantum computers, and are more of a diagnosis of where our understanding of quantum computation is currently lacking than an imminent practical threat. “It’s like a nightmare scenario that would be very bad if it happened,” he says. “Maybe it won’t, but we have to understand it better.”

Bill Fefferman Researchers from the University of Chicago in Illinois say the course opens up interesting questions about what computers in general can do. “This may point to the limits of computing more broadly, that despite achieving significant speedups for certain specific tasks, there will always be tasks that are still too difficult even for efficient quantum computers,” he says.

Mathematically, the new study links aspects of quantum information science used in quantum cryptography with fundamental ideas of matter physics, so it could also help advance both, he says.

Going forward, the team wants to expand their analysis to include quantum phases of matter that are more energetic or exciting, which are notoriously difficult to calculate on a larger scale.