Advancing simulations with quantum computing

Although ‘coupled oscillations’ may not sound familiar, they are ubiquitous in nature. The term “coupled harmonic oscillators” describes interacting systems of masses and springs, but their usefulness in science and engineering doesn’t end there. They describe mechanical systems such as bridges, the connections between atoms, and even gravitational tidal effects between the Earth and the moon. Understanding such problems allows us to explore a correspondingly vast range of systems, from chemistry to engineering to materials science and beyond.

Classically represented by a ball and spring model, coupled oscillating systems become increasingly complex as more oscillators are added. With a new quantum algorithm developed in part by Pacific Northwest National Laboratory (PNNL) co-author and University of Toronto professor Nathan Wiebe, simulating such complex coupled oscillator systems is now faster and more efficient. These results were published in Physical Assessment X.

In collaboration with researchers from Google Quantum AI and Macquarie University in Sydney, Australia, Wiebe developed an algorithm for simulating systems of coupled masses and springs on quantum computers. The researchers then provided evidence of the new algorithm’s exponential advantage over classical algorithms.

This acceleration was made possible by mapping the dynamics of the coupled oscillators with a Schrödinger equation – the quantum counterpart of a classical Newtonian equation. From there, the system could be simulated using Hamiltonian methods.

Essentially, this approach allows scientists to express the dynamics of coupled oscillators using far fewer quantum bits than traditional methods. Researchers can then simulate the system with exponentially fewer operations.

Perhaps the most intriguing aspect of their work comes from the question of whether this algorithm indeed provides exponential speedup over all possible regular algorithms. First, the authors showed that this algorithm works both ways: that coupled harmonic oscillators can be used to simulate an arbitrary quantum computer.

This means that at a high level, very large systems of interacting masses and springs can contain computing power comparable to that of a quantum computer.

Second, the authors took into account the theoretical limitations around calculating these dynamics. If there were a way to simulate these dynamics in polynomial time on existing computers, then researchers could construct a faster method for simulating quantum computers. However, this would prove that quantum computers are essentially no more powerful than classical computers.

The evidence gathered over the years shows that it is exceptionally unlikely that classical computers are as qualitatively powerful as quantum computers. This work thus provides a compelling argument that this algorithm enables exponential acceleration, as well as a clear demonstration of a new and subtle connection between quantum dynamics and the simple harmonic oscillator.

“Very few new classes of demonstrable exponential accelerations of classical computation have been developed,” says Wiebe. “Our work provides a significant computational advantage for a wide range of problems in engineering, neuroscience and chemistry.”