A leading use for quantum computers might not need them after all

As quantum computers continue to advance, identifying problems they can solve faster than the world’s best conventional computers is becoming increasingly important – but it turns out that a key task held up as a future goal by quantum proponents may not need a quantum computer at all.

The task in question involves a molecule called FeMoco, which plays a vital role in making life on Earth possible. That is because it is part of the process of nitrogen fixation, in which microbes convert atmospheric nitrogen into ammonia, making it biologically accessible to most other living organisms. How exactly FeMoco works during this process is complicated and not fully understood, but if we could crack it and replicate it on an industrial scale, it could drastically cut the energy involved in producing fertilisers, potentially leading to a boost in crop yields.

One key aspect of understanding FeMoco is determining its lowest, or “ground-state”, energy, which involves accounting for the behaviour of its many electrons. But electrons are quantum particles that can behave in wave-like ways and occupy many different regions called orbitals. This level of complexity – with many electrons in many orbitals – is why computing lots of FeMoco’s properties has, so far, been intractable with conventional computers.

Researchers have had some success using approximation methods, but the accuracy of their energy estimates remained limited. On the other hand, mathematical investigations have rigorously proven that quantum computers, which encode this complexity in a fundamentally different manner, could solve the problem without approximations – a well-established example of so-called quantum advantage.

But now, Garnet Kin-Lic Chan at the California Institute of Technology and his colleagues have found a conventional computing method that seems to be able to reach the same accuracy as a quantum one. The key metric has been the idea of “chemical accuracy”, or the minimal accuracy required to make realistic predictions for chemical processes. Based on their computations, Chan and his colleagues argue that conventional supercomputers can calculate FeMoco’s ground-state energy to that accuracy too.

FeMoco has many quantum states, each of which has its own energy, and they are arranged on something like a ladder with the ground state at the very bottom. To make reaching that bottom rung more amenable to classical computer algorithms, the researchers focused on what we know about states that sit on nearby rungs and what their properties imply about what can exist a step or two below. This included, for example, insights about symmetries of electrons’ quantum states.

Ultimately, the simplification allowed the researchers to use classical algorithms to calculate upper bounds for FeMoco’s ground-state energy, then mathematically extrapolate them to an energy value with an uncertainty that matches chemical accuracy. In other words, their final answer for what the molecule’s lowest energy can be ought to be precise enough to use in future studies.

The researchers also estimated that the supercomputer method may even be faster than quantum ones, performing calculations in less than a minute that would take 8 hours on a quantum device – although this estimate assumes an ideal supercomputer performance.

So, does that mean we will soon understand FeMoco well enough to boost agriculture? Not quite – there are still many unanswered questions about, for instance, which parts of the molecule interact with nitrogen the most or what molecules may be produced as intermediate steps in the nitrogen-fixation process.

“The work doesn’t really tell us much about the FeMoco system in terms of its function, but as a model to show quantum advantage, it does place the bar even higher for quantum approaches,” says David Reichmann at Columbia University in New York.

Dominic Berry at Macquarie University in Sydney, Australia, points out that while the team’s work shows that classical computers can attack the FeMoco problem, they are still only capable of approximation, while quantum methods guarantee that the problem can be solved in full.

“This does challenge the argument for using quantum computers for problems like this, but for more complicated systems, it is expected that the computation time for classical methods will increase much faster than that for quantum algorithms,” he says.

Another issue is that quantum computers are still improving. Existing quantum computers are all too small and error-prone to tackle problems like FeMoco’s ground-state energy, but a new generation of fault-tolerant quantum computers, which are able to correct their own errors, is expected soon. In practical terms, they may still be the best way to understand FeMoco and related molecules, says Berry. “Quantum computing should enable these systems to be solved far more generally, making it a routine calculation when fault-tolerant quantum computers are available.”