Quantum neural network may be able to cheat the uncertainty principle

Heisenberg’s uncertainty principle places a limit on the precision with which we can measure certain properties of quantum objects. But researchers may have found a way around this limitation by using a quantum version of a neural network.

Given, for example, a chemically useful molecule, how can you predict what properties it might have in an hour or tomorrow? To make such predictions, researchers start by measuring its current properties. But for quantum objects, including some molecules, this can be surprisingly difficult, because each measurement can interfere with or change the result of the next measurement. Notably, Heisenberg’s uncertainty principle states that certain quantum properties of objects simply cannot be precisely measured simultaneously. For example, if you measure the momentum of a quantum particle extremely well, measuring its position will only return an approximate number.

Now, Duanlu Zhou of the Chinese Academy of Sciences and colleagues have mathematically proven that using quantum versions of a neural network can avoid some of these difficulties.

Zhou’s team explored the problem for practical reasons. When researchers use quantum computers, they need to know the properties of the computer’s building blocks, called qubits, either to evaluate and compare the device or to effectively use those qubits when emulating an object like a molecule or material. To determine the properties of a qubit, researchers typically apply certain operations, similar to those applied to “divide by 2” to determine whether a number is even. But the uncertainty principle means that some of these operations will be incompatible – the equivalent of not being able to multiply a number by three and then divide it by two and that calculation still return a meaningful answer.

The researchers’ calculations now show that the incompatibility problem can be solved if a quantum machine learning algorithm – a quantum neural network (QNN) – is applied instead of simpler operations.

It is important to note that some steps of this algorithm must be chosen randomly from a predetermined set. Previous studies showed that such randomness could make QNNs more effective at determining a single property of a quantum object, but Zhou and his colleagues extended the idea to measuring multiple properties, including combinations of properties normally constrained by the uncertainty principle. They could do this because the results of many consecutive random operations can be disentangled using special statistical methods to produce more accurate results than when a single operation is performed repeatedly.

Robert Huang of the California Institute of Technology says that being able to effectively measure many incompatible properties means that scientists will be able to learn much more quickly about a given quantum system, which is important for applications of quantum computers in chemistry and materials science – as well as for understanding increasingly larger quantum computers themselves.

The new approach could presumably be implemented in practice, but its success will depend on how useful it is compared to similar approaches that also exploit randomness to make informative quantum measurements, Huang says.