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The following text has been machine translated from the German and has undergone no postediting.
When Jonas Haferkamp tries to explain what he discovered in his latest paper, published in the renowned journal Science, he uses a cup of coffee as an analogy: ‘For example, if I pour some milk into my coffee, after a short time I can still guess where the milk hit the coffee. But if I wait a few minutes, it's just brown, and the information about the initial configuration has effectively disappeared,’ says the junior professor of quantum information theory at Saarland University. ‘Theoretically, the atoms still contain the information about the initial configuration. But how can you ever extract it from the mixture?’ asks the mathematician. And he immediately adds: ‘What we found in our work is that there is an effect in quantum mechanics that acts like stirring coffee. The chaotic states occur incredibly quickly.’
This analogy helps to understand what Jonas Haferkamp and his colleagues Thomas Schuster and Hsin-Yuan Huang from the California Institute of Technology have recently discovered: a phenomenon from the quantum world that no one has observed before, or rather that no one expected, and which could help to take quantum technologies based on random measurements, for example, to a new level.
First things first: coffee and milk do not play a role in Jonas Haferkamp's work, of course. However, the two substances symbolise what he and his colleagues describe mathematically: the random and highly complex interactions between ‘coffee particles’ and ‘milk particles’. Similar to how coffee and milk form a chaotic and indissoluble unit, particles such as atoms, photons or electrons behave in the same way when they reach a typical quantum state. Any efficient measurement will only provide averaged generic answers that allow hardly any conclusions to be drawn about the actual state.
The generation of random quantum states is of practical relevance for new quantum technologies. In a quantum computer with a few qubits, the equivalent of bits on conventional computers, as was still feasible in research a few years ago, this randomness was not a huge problem in principle. The ‘depth’ of the circuits between the qubits, i.e. the complexity of their interaction, is not yet insurmountably high with a small number of qubits.
However, with quantum computers that now have several hundred qubits as computing units, the difficulty of achieving purely random quantum states increases exponentially. Even a fully functional quantum computer would quickly reach its limits.
‘We have now discovered a phenomenon that could help reduce this complexity,’ explains Jonas Haferkamp. Essentially, he and his colleagues use a ‘mathematical trick’ to simulate the complexity of the network of relationships between the individual particles. In practice, this involves taking a ‘truly randomised matrix’, which is created when a process involving quantum particles and their random, chaotic interactions with each other is described mathematically, and turning it into a ‘pseudo-randomised matrix’ that only pretends to describe a random quantum mechanical process. The new method for generating such pseudo-random processes can be implemented very quickly using quantum computers. In mathematics, this is referred to as a system having less depth or being ‘flatter’. The bottom line is that it is less complex and therefore easier to generate.
Jonas Haferkamp spent years researching similar problems as a doctoral student and postdoc until he and his US colleagues discovered this phenomenon, which was considered unlikely by experts in the field. ‘Actually, many in our field were convinced that this type of pseudo-randomness only occurs at much greater depth,’ says the mathematician, summarising the state of research, which was considered consensus until his publication.
The consequences of this discovery could be far-reaching. If these mathematical rules can be applied to technical systems, it could mean a significant improvement for many quantum technologies, as these ‘pseudo-randomised’ (flat) circuits cannot be distinguished from genuine randomised (deep) ones from the outside. Even on smaller quantum computers, this type of random process could soon help to extract information from quantum experiments or enable the development of new encryption methods that were not yet feasible with previous methods.
Original publication:
Thomas Schuster et al., Random unitaries in extremely low depth. Science389, 92-96 (2025). DOI: 10.1126/science.adv8590
Further information:
Jun.-Prof. Dr Jonas Haferkamp
Email: haferkamp(at)math.uni-sb.de
