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Caltech professor of chemistry Sandeep Sharma and colleagues from IBM and the RIKEN Center for Computational Science in Japan are giving us a glimpse of the future of computing. The team has used quantum computing in combination with classical distributed computing to attack a notably challenging problem in quantum chemistry: determining the electronic energy levels of a relatively complex molecule.

The work demonstrates the promise of such a quantum–classical hybrid approach for advancing not only quantum chemistry, but also fields such as materials science, nanotechnology, and drug discovery, where insight into the electronic fingerprint of materials can reveal how they will behave.

"We have shown that you can take classical algorithms that run on high-performance classical computers and combine them with quantum algorithms that run on quantum computers to get useful chemical results," says Sharma, a new member of the Caltech faculty whose work focuses on developing algorithms to study quantum chemical systems. "We call this quantum-centric supercomputing."

The team first used an IBM quantum device, powered by a Heron quantum processor, to simplify the mathematics and then used RIKEN's Fugaku supercomputer to solve the problem. They used as many as 77 qubits (quantum bits) in the process. Most previous quantum computing experiments for studying chemical systems have only managed to use a few qubits.

The work in the current issue of the journal Science Advances and is featured on the cover.

In the new study, the scientists wanted to use quantum computing to investigate an iron–sulfur system, the [4Fe-4S] molecular cluster, that is an important component of many reactions that take place in biology. For example, the iron–sulfur cluster appears to play a central role in the enzyme nitrogenase, which is responsible for nitrogen fixation—the conversion of atmospheric nitrogen gas into ammonia that makes it possible for plants to grow.

Solving for a system's wave function

In quantum chemistry, a key value that unlocks all kinds of information about a system is the ground state, the lowest possible energy level of a system. If chemists want to figure out whether a system such as the [4Fe-4S] molecular cluster is reactive, determine its stability, or learn how it will behave as a catalyst, for example, they first need to know the ground state.

In this state, a mathematical representation called a wave function describes the probability that the electrons in the system will be in a particular location. Solving a quantum-mechanical equation called Schrodinger's equation yields this wave function.

Many classical algorithms struggle to solve the correct wave function of the [4Fe-4S] molecular cluster.

Over the last decade, it has become something of a mantra in the field of quantum computing that solving for the wave function of such iron–sulfur molecular clusters using a quantum algorithm will demonstrate that quantum algorithms can outperform their classical counterparts.

"The current paper doesn't quite get us to the point where you can definitively say that we are better than any classical algorithm, but it's quite a bit beyond what anybody else has done using quantum algorithms in the past, " Sharma says.

Quantum can identify the important values in a matrix

Scientists typically provide a classical algorithm with all of the known information about a system—how many electrons are in the system, the position of the atoms, etc. Based on that information, an algorithm creates an enormous matrix known as the Hamiltonian. Its size increases exponentially with each additional electron in a system.

"You can imagine that very quickly, you run out of computing steam," says Sharma.

But many of the values within these matrices are not crucial for calculating the system's wave function. So typically, classical algorithms turn to a type of approximation called classical heuristics to prune down the matrix—to come up with a smaller, more manageable subset of representative values that is easier to work with. Sometimes the approximations work, sometimes they don't.

"This paper demonstrates that those classical heuristics can be replaced by something a bit more rigorous that comes from a quantum computer," Sharma explains. "Now, instead of using classical heuristics, a quantum computer is telling us what the most important components in the matrix are."

From there, the scientists fed the most relevant part of the Hamiltonian matrix into the RIKEN supercomputer to solve for the exact wave function.