Mario Krenn, a quantum physicist, recalls sitting at a Vienna café in early 2016 reading through computer printouts, trying to make sense of what MELVIN had discovered. MELVIN was a sort of artificial intelligence created by Krenn using a machine-learning algorithm. Its mission was to mix and match the components of typical quantum experiments to solve novel issues. I did find a lot of interesting ones. However, there was an illogical one.
“The first thing that sprang to mind was, ‘My program must have a bug because the answer cannot exist,’” explains Krenn. MELVIN appeared to have solved the difficulty of producing highly complex entangled states involving numerous photons (entangled states being those that once prompted Albert Einstein to utter the phrase “spooky action at a distance”). MELVIN had discovered a method even though Krenn and his colleagues had not explicitly given it the rules it needed to build such complicated situations. He eventually understood that the algorithm had unearthed an early 1990s experimental arrangement. Those experiments, on the other hand, had been much easier. MELVIN had solved a significantly more difficult puzzle.
“Once we figured out what was going on, we were able to generalize [the answer] right away,” says Krenn, who currently teaches at the University of Toronto. Since then, other teams have begun to replicate MELVIN’s experiments, allowing them to test quantum mechanics’ conceptual underpinnings in novel ways. Meanwhile, Krenn, University of Vienna’s Anton Zeilinger, and their colleagues have improved their machine-learning algorithms. Their most recent effort, THESEUS, has upped the ante: it is orders of magnitude faster than MELVIN, and its output is easily parsable by humans. While it would take Krenn and his colleagues days or even weeks to figure out MELVIN’s ramblings, they can figure out what THESEUS is saying nearly instantly.
“It is great to work,” says Renato Renner of the Swiss Federal Institute of Technology Zurich’s Institute for Theoretical Physics, who studied a 2020 research about THESEUS by Krenn and Zeilinger but was not actively involved in their efforts.
When Krenn and his colleagues were trying to figure out how to experimentally construct quantum states of photons entangled in a specific way, they stumbled into this entire research program by chance. When two photons collide, they become entangled and can only be formally described using a single quantum state. Even if the two photons are thousands of kilometers distant, measuring the state of one fixes the state of the other (thus Einstein’s dismissive remarks about entanglement being “spooky”).
Daniel Greenberger, the late Michael Horne, and Zeilinger, three physicists, described an entangled state known as “GHZ” in 1989. (after their initials). It involved four photons, each of which might be in a quantum superposition of two states, such as 0 and 1, for example (a quantum state called a qubit). The GHZ state, according to their study, entailed entangling four qubits to create a two-dimensional quantum superposition of states 0000 and 1111. The superposition would collapse if one of the photons was found to be in state 0, and the other photons would also be in state 0. The same may be said about state 1. For the first time, Zeilinger and his colleagues used three qubits to observe GHZ states in the late 1990s.
Krenn and his colleagues were looking for higher-dimensional GHZ states. They planned to operate with three photons, each of which had a dimensionality of three, which meant it could be in any of three states: 0, 1, or 2. A qutrit is a name for this quantum state. The three-dimensional GHZ state that the researchers were looking for was a superposition of states 000, 111, and 222. These states are necessary for secure quantum communications and quicker quantum computation. The researchers spent weeks in late 2013 developing experiments on blackboards and performing computations to see if their setups could produce the requisite quantum states. Each time, though, they failed. “I thought to myself, ‘This is absurd.’ ‘Why can’t we come up with something?’ says Krenn.
Krenn first built a computer program that took an experimental setting and estimated the output to speed up the process. Then he updated the computer to include in its calculations the same building elements that experimenters use on an optical bench to make and control photons: lasers, nonlinear crystals, beam splitters, phase shifters, holograms, and so on. By randomly mixing and matching the building parts, the program searched through a huge space of combinations, did the computations, and vomited out the outcome. MELVIN was conceived. “Within a few hours, the software had discovered a solution that we scientists—three experimentalists and one theorist—had been unable to find for months,” Krenn adds. “That was a hectic day,” says the narrator. I couldn’t believe it had happened to me.”
Then he boosted MELVIN’s intelligence. MELVIN added new setups to its toolbox whenever it discovered one that was useful. “The algorithm remembers it and tries to apply it to more complicated problems,” Krenn says.
In a Viennese café, Krenn was left scratching his head by this highly advanced MELVIN. He’d started it up with an experimental toolbox containing two crystals, each capable of producing a pair of entangled photons in three dimensions. MELVIN would identify configurations that paired these pairs of photons to form entangled states with at most nine dimensions, according to Krenn’s naive expectation. But, as Krenn points out, “it found one solution, an exceedingly rare instance, with substantially higher entanglement than the rest of the states.”
MELVIN had adopted a strategy that many teams had devised nearly three decades ago, he eventually discovered. Xin Yu Zou, Li-Jun Wang, and Leonard Mandel, all of whom were at the University of Rochester at the time, devised one way in 1991. In 1994, Zeilinger and his colleagues at the University of Innsbruck in Austria devised a new method. These trials attempted something similar in concept, but Zeilinger and his colleagues produced a setup that is easier to understand. It all starts with a single crystal that produces two photons (A and B). These photons’ paths pass right through another crystal, which can yield two photons as well (C and D). Photon A from the first crystal and photon C from the second crystal have identical trajectories and lead to the same detector. It’s hard to distinguish whether the photon came from the first or second crystal if that detector clicks. Photons B and D are the same way.
A phase shifter is a device that increases the route taken by a photon by a fraction of its wavelength. You might produce constructive and destructive interference at the detectors if you put a phase shifter in one of the pathways between the crystals and continuously altering the degree of phase shift. Each of the crystals could, for example, produce 1,000 pairs of photons every second. The detectors would register 4,000 pairs of photons per second if constructive interference was used. They would detect none with destructive interference since the device as a whole would not produce any photons despite individual crystals creating 1,000 pairs per second. “When you think about it,” Krenn continues, “that is rather crazy.”
Such overlapping routes were part of MELVIN’s unusual solution. The fact that the algorithm only had two crystals in its toolbox had perplexed Krenn. It had wedged the crystals inside an interferometer instead of using them at the start of the experimental setup (a device that splits the path of, say, a photon into two and then recombines them). He understood that the configuration MELVIN had discovered was equivalent to one using more than two crystals, each emitting pairs of photons, and their routes to the detectors overlapping after much effort. The arrangement could be used to create entangled states with several dimensions.
Nora Tischler, a quantum physicist who was a Ph.D. student working with Zeilinger on an unrelated topic at the time MELVIN was being tested, was keeping an eye on the developments. “It was evident from the start that such an experiment would not exist unless it was discovered by an algorithm,” she explains.
The setup involving more than two crystals with overlapping routes can be used to perform a generalized version of Zeilinger’s 1994 quantum interference experiments with two crystals, in addition to generating complicated entangled states. The AI’s findings have impressed Aephraim Steinberg, an experimentalist at the University of Toronto who is a Krenn colleague but has not worked on these projects. “This is a generalization that no human (to my knowledge) conceived up in the preceding decades and may never have done,” he says. “It’s a stunning initial indication of the new frontiers that thinking machines can open up for us.”
Quantum interference can cause circumstances where all four detectors click (constructive interference) or none of them click (nonconstructive interference) in a generalized configuration with four crystals each generating a pair of photons and overlapping pathways leading to four detectors (destructive interference).
However, carrying out such an experiment had remained a faraway fantasy until lately. Then, in a March preprint paper, a team led by Lan-Tian Feng of the Chinese University of Science and Technology, in partnership with Krenn, stated that they had built the entire system on a single photonic chip and carried out the experiment. The researchers were able to collect data for almost 16 hours thanks to the photonic chip’s exceptional optical stability, which would have been hard to achieve in a larger-scale tabletop experiment. For starters, Steinberg says the arrangement would necessitate a square meter of optical elements precisely positioned on an optical bench. Furthermore, “a single optical element jittering or drifting by a thousandth of a human hair diameter during those 16 hours could be enough to wash out the effect,” he claims.
Krenn and his colleagues observed that the solution resembled abstract mathematical shapes called graphs, which have vertices and edges and are used to illustrate pairwise relations between objects, during their early attempts to simplify and generalize what MELVIN had discovered. Every path a photon takes is represented by a vertex in these quantum experiments. An edge connecting two vertices, for example, represents a crystal. MELVIN created such a graph before applying a mathematical procedure to it. The “perfect matching” operation entails creating an equivalent graph with each vertex connected to only one edge. Although this procedure makes computing the final quantum state considerably easier, it is still difficult to comprehend for humans.
That changed with MELVIN’s successor THESEUS, which builds considerably smaller networks by whittling down the first complicated graph it finds to the bare minimum of edges and vertices (to the point where any more deletion damages the setup’s capacity to generate the necessary quantum states). Because such graphs are simpler than MELVIN’s perfect matching graphs, any AI-generated solution is even easier to understand.
THESEUS’s human-interpretable outputs particularly impress Renner. “The technique is aimed to minimize the number of connections in the graph,” he explains. “And that, of course, is a solution we can understand better than if you had a very complicated graph.”
The work impresses Eric Cavalcanti of Griffith University in Australia, but he is cautious about it. “These machine-learning methods are a fascinating development. Some of the solutions may appear to be “creative” new solutions to a human scientist looking at the data and interpreting it. But, at this point, these algorithms are still a long way from coming up with truly novel ideas or concepts,” he says. “On the other hand, I believe they will get there one day. So, while they are small steps, we must begin somewhere.”
Steinberg concurs. He describes them as “wonderful instruments” for the time being. “And, like all good tools, they’re already allowing us to do things we wouldn’t have been able to do without them.”