How Many-to-Many is Too Many for Many-Body Quantum Systems?

Excellent read for those looking to broaden their knowledge of entanglement. Difficult to capture in a few short notes or excerpts. Recommend the entire piece from the source, below. Because Quantum is Coming. Qubit.

Many’s Not Too Many Anymore for Quantum Systems

Excerpts and salient points ~

+  A quarter-century ago, the problem of understanding a system of many correlated electrons seemed intractable. Even under the onslaught of the most powerful computers, only a few specific cases could be solved.

Two-particle Entanglement

+  Today, this picture has changed. Steady progress in computer hardware and software in the past 25 years has helped, but ‘Moore’s law’ is no match on its own for the barriers posed by the quantum states of a throng of electrons. More important are new insights into the problem itself. According to Andy Millis, co-director of the Simons Collaboration on the Many Electron Problem and the Flatiron Institute’s Center for Computational Quantum Physics (CCQ), if there is one overarching insight driving recent progress, it is the more sophisticated understanding researchers have achieved about a uniquely quantum-mechanical phenomenon called entanglement.

Describing many-body quantum systems is generally next to impossible, physicists thought — until they realized that localized entanglement holds the key.

+  When particles are entangled, their states become weirdly linked in a way that has no exact analogue in the classical physics that describes our everyday reality. In the field of quantum computing, researchers are striving to design and build devices that exploit entanglement’s remarkable properties as a resource and enable new types of computation. For theorists working on the many-electron problem, however, entanglement represents a barrier to be overcome. The powerful insight they’ve gained, Millis explains, “is that entanglement is physical, and you should pay attention to it.”

+  A different approach focuses more directly on isolating a very small subsystem. This ‘quantum embedding’ technique involves performing detailed, full calculations for the subsystem with the remainder of the system serving as an environment whose effects are approximated in these calculations. The subsystem might be as small as a single electron orbital on a particular copper atom in a superconductor. Antoine Georges, the director of CCQ and the collaboration, invented one of the most important methods along these lines.

+  Another fascinating possibility is to use artificial neural networks. The problem of the huge space of highly entangled states containing a much smaller space of interest, with locally entangled states, is analogous to the problems that neural networks have proved very adept at solving in recent years, such as recognizing speech or thoroughly defeating the world champion at the game of Go. For the many-electron problem, a neural network could find and operate in the low-dimensional subspace of interest for a given system in an automated fashion. This approach was demonstrated in 2017 for one particular many-body problem by Giuseppe Carleo and Matthias Troyer of ETH Zurich (Carleo has subsequently joined CCQ). A surge of intense interest and additional work by many researchers has followed.

Source:  SF.  Simons Foundation,  Many’s Not Too Many Anymore for Quantum Systems…

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