The Quest to Decipher the Super Equation of Quantum Systems

Tuesday - May 7 2024, 23:31 UTC - 6 months ago

Physicists have developed a new algorithm that can efficiently calculate the unique equation for each quantum system, called the Hamiltonian, using sample measurements. This breakthrough could help understand exotic quantum phenomena like superconductivity and superfluidity. However, the algorithm currently only works for systems at high temperatures.

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.

The new result is the fruit of several years' worth of scientific labor. Prior research by Anshu and others got part of the way there. Those researchers developed an algorithm that could deduce a system's Hamiltonian using a reasonable amount of sample data: The amount needed increased only as a polynomial function of the number of particles.

However, the approach was not computationally efficient -- even though it didn't require too much data, it still took too long to calculate to be practical. The next question was clear: "Is there any setting in which you could get something fast?" said Ewin Tang, a theoretical computer scientist at Berkeley and one of the new paper's co-authors.

It turned out the answer was yes -- Tang and others soon found an optimal algorithm for learning a system's Hamiltonian that was polynomial in runtime. But again, there was a catch. The algorithm only worked for high-temperature settings, so it only partially resolved the open question.

"The caveat is that most of the exotic [quantum] phenomena we know are interesting precisely because they occur at low temperatures," Wang said.