Quantum many-body problem solved to order 15

The finding is a major one for theoretical physics: Researchers from Irig, Institut Néel, and the Flatiron Institute (US) designed an algorithm that solves the quantum many-body problem to order 15.

The quantum many-body problem describes phenomena at the atomic scale that standard approaches (“mean field approximation”) cannot model. One such example is the fact that cuprates, electrically-conductive materials, become superconducting at temperatures as high as 160 K. The solution, however, is hampered by the number of operations. For order 3 processes, the reciprocal influences between three bodies must be calculated; for order 4 processes it is between four bodies, and so on. At order 15, the computer must complete a staggering 1,000 billion operations!

New algorithm successfully makes the jump from order 7 to order 15

Previously, the huge number of operations meant that only processes up to order 7 or so could be solved. Irig’s algorithm lightens the computing load drastically, coming in at just 32,768 operations for order 15 processes. The algorithm delivered the first-ever accurate numerical solution to the non-equilibrium Kondo effect, a behavior specific to certain electrical conductors at low temperatures.

The researchers are still investigating the possibilities this algorithm will create. They have already identified several potential uses in quantum computing. In effect, the quantum many-body problem can very accurately describe the physics of an actual set of qubits, beyond the extremely-simplified forms used by mathematicians.

Contact: xavier.waintal@cea.fr

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