Synopsis

Making Quantum Computations Behave

Physics 11, s81
A new computational method tackles many-body quantum calculations that have defied a suite of existing approaches.

Calculations of a quantum system's behavior can spiral out of control when they involve more than a handful of particles. So for just about anything more complicated than the hydrogen atom, physicists forget about finding an exact solution to the Schrödinger equation and rely instead on approximation methods. Dean Lee of Michigan State University, East Lansing, and colleagues have now proposed an alternative method for when even the best approximation schemes fail. Their approach should be applicable to a variety of many-particle problems in atomic, nuclear, and particle physics.

The researchers considered the popular Bose-Hubbard model to illustrate their idea.​ In the model, which has been used to describe atoms in an optical lattice and in superconductors, bosons hop from point to point on a cubic grid, but they interact with one another only when they sit on the same site. Physicists are interested in how the particles behave as the strength of this interaction, U, varies. Using the so-called perturbative approach, the particles’ wave function can be calculated for a simple case ( U=0) and then approximated at greater interaction strengths in terms of a power series in U. But this formula blows up when U is too large.

Instead, the team’s approach was to track the wave function’s changing shape at a few values of U where the functions can be accurately calculated. They then used this shape “trajectory” to predict the ground-state wave function at values of U that perturbation theory can’t reach, demonstrating the accuracy of their method for four bosons on a 4×4×4 grid.

Lee says the technique, which he and his colleagues have dubbed “eigenvector continuation,” should work well for calculations that involve a smoothly varying parameter, like interaction strength, but it might struggle with a discretely varying parameter, like particle number. The researchers are now planning to dive into some computations that are known to defy conventional methods, such as simulations involving large nuclei.

This research is published in Physical Review Letters.

–Jessica Thomas

Jessica Thomas is the Editor of Physics.


Subject Areas

Computational PhysicsAtomic and Molecular PhysicsNuclear Physics

Related Articles

Time Delays Improve Performance of Certain Neural Networks
Computational Physics

Time Delays Improve Performance of Certain Neural Networks

Both the predictive power and the memory storage capability of an artificial neural network called a reservoir computer increase when time delays are added into how the network processes signals, according to a new model. Read More »

Ocean Currents Resolved on Regional Length Scales
Computational Physics

Ocean Currents Resolved on Regional Length Scales

Using a detailed simulation, researchers reveal how climate change will affect the regional dynamics of the conveyor-belt-like circulation of water through the Atlantic Ocean. Read More »

Predicting Tipping Points in Complex Systems
Computational Physics

Predicting Tipping Points in Complex Systems

A machine-learning framework predicts when a complex system, such as an ecosystem or a power grid, will undergo a critical transition. Read More »

More Articles