Physicists have done a remarkable job explaining the chaos of the universe with well-behaved equations, but certain situations remain mysterious. Among these are collections of many tiny particles — they can be atoms, electrons, anything sufficiently small — that interact in surprising and complicated ways. These interactions give rise to exotic quantum phenomena including superconductivity (in which materials conduct electricity without losing energy), superfluidity (the frictionless flow of a fluid) and topological order (where particles interact according to a strict choreography).
Theoretically, there is a way to understand these various behaviors, a kind of super equation unique to each quantum system that can fully describe the system’s physical properties. Unfortunately, real-life systems are so complicated that it’s often impossible to write down this equation, called a Hamiltonian, ahead of time.
Instead, researchers have become experts at the inverse problem: If we can measure the properties of a given system, can we deduce its Hamiltonian?
This problem is known to be computationally difficult. Any algorithm that can take measurements of a system and return the specific Hamiltonian has always required too many measurements to be efficient. Or it takes too long to be practical.
But late last year, four co-authors from the Massachusetts Institute of Technology and the University of California, Berkeley shared a new algorithm that can spit out the Hamiltonian of any quantum system at any constant temperature. It’s efficient in both sample size and runtime, so it doesn’t require too many measurements, nor does it take too long to calculate. It’s the first time researchers have been able to quickly and accurately discern a given system’s Hamiltonian. This work was named best student paper by the Quantum Information Processing conference for its only student author, Allen Liu.
“This is a very exciting result,” said Anurag Anshu, a computer scientist at Harvard University who was not involved with the research. “They gave the first very important step in computational learning” of the Hamiltonian.
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