Mario Klein, a quantum physicist, still remembers when he browsed through MELVIN's calculation results in a cafe in Vienna in early 2016. MELVIN is a set of machine learning algorithms created by Klein, which is a kind of artificial intelligence. Its task is to mix and compare the basic modules of various standard quantum experiments to find solutions to new problems. Crane discovered that MELVIN did make many interesting discoveries, but one of them made him puzzled.

  "My first reaction at the time was,'My program must have a bug,' because this solution simply cannot exist." MELVIN seems to want to solve the problem by creating a complex entangled state of multiple photons. The problem is that Klein, Anton Salinger and their colleagues did not provide MELVIN with the rules needed to create such complex quantum states, but MELVIN found a solution on his own. In the end, Klein realized that what the algorithm discovered was actually a set of experimental arrangements designed in the early 1990s, but the original set of experiments was much simpler, and the problem that MELVIN solved was far more complex.

  "After we understood what this was all about, we immediately summarized and generalized this solution." Crane said. Since then, other teams have also carried out some new experiments designed by MELVIN to test the theoretical basis of quantum mechanics in a brand new way. At the same time, Klein moved from the University of Vienna to the University of Toronto, and worked with new colleagues to improve their machine learning algorithms. They recently developed an artificial intelligence system called THESEUS. Not only the calculation speed is several orders of magnitude faster than MELVIN, but the calculation results are clear to humans. The calculation results of MELVIN need days or even days to understand by Klein and his colleagues, but the calculation results of THESEUS are almost self-evident at a glance.

  Crane came into contact with this research project by accident. At that time, he and his colleagues wanted to figure out how to create a quantum entangled state of photons through experiments: when two photons interact, an "entanglement" relationship is formed, and the two photons involved can only pass through the same quantum state. Perform mathematical description. If you measure the state of one of the photons, even if the two photons are thousands of miles apart, the measurement result can be consistent with the other photon (hence Einstein called it a "spiritual entanglement").

  In 1989, three physicists, Daniel Greenberg, Michael Horn and Salinger, described a quantum state called GHZ (the combination of the initials of the three people's surnames). The GHZ quantum state involves four photons, and each photon is in a superposition state of 0 or 1 (this kind of quantum state is called a qubit). In the paper published by the trio, the GHZ state contains four entangled qubits, and the entire system is in a two-dimensional quantum superposition state, either 0000 or 1111. If one of the photons is measured and found to be in state 0, the entire superposition state will collapse, and the state of the other photons is also 0; the same is true for the measured result of 1. In the late 1990s, Salinger and his colleagues observed the GHZ state of three qubits for the first time in an experiment.

  Crane and his colleagues also want to observe higher-dimensional GHZ states. They want to use three photons, each of which has three dimensions, that is, it can be in a superposition state of 0, 1, and 2. This kind of quantum state is called a "three-dimensional qubit. What Klein's team is looking for is a three-dimensional GHZ state in the superposition state of 000, 111, and 222. This quantum state can greatly enhance the quantum communication Security, and the speed of quantum computing. At the end of 2013, researchers spent several weeks designing experiments and carrying out calculations, trying to create the required quantum states through experiments, but each time they failed. Klein said: " I was mad at the time, why can't we find the correct experimental setup? "

  In order to speed up the research process, Klein first wrote a set of computer programs that can calculate the experimental results according to the experimental settings, and then upgraded the program to integrate the basic modules used to generate and manipulate photons on the optical test bench. Including lasers, nonlinear optical crystals, beam splitters, shifters, holograms, etc. This set of programs randomly mixes and matches these modules, combines them into a large number of configurations, and performs calculations and outputs the results in turn. MELVIN was born. "In just a few hours, this program found a solution that we scientists had not been able to find for months." Crane pointed out, "It was a crazy day. I still can't believe it. It really happened."

  Next, he gave MELVIN more wisdom. Every time it finds a useful configuration, MELVIN will add it to its "toolbox". "This algorithm will remember these and try to use them to find more complex solutions."

But what made Klein puzzling in the café in Vienna was the "evolved" MELVIN. In MELVIN's experimental "toolbox", Klein added two crystals, each of which can produce a pair of photons in a three-dimensional entangled state. Crane originally thought that MELVIN would find an experimental configuration that could combine these two sets of photons together in up to 9 dimensions. But "it actually found a very rare solution, the degree of entanglement is much higher than other quantum states."

　　Crane finally discovered that MELVIN actually uses a technology developed by several research teams nearly thirty years ago. In 1991, three researchers from the University of Rochester devised one of these experimental methods. Then in 1994, Salinger and colleagues at the University of Innsbruck in Austria devised another one. From a conceptual point of view, the results of these experiments are similar, but the experimental configuration designed by Salinger is simpler and easier to understand. In this experiment, one crystal generates a set of photons (A and B), and the travel path of these two photons will pass through another crystal to produce photons C and D. The travel paths of the photon A emitted from the first crystal and the photon C emitted from the second crystal will completely overlap and will reach the same detector. Therefore, the detector cannot determine whether a photon comes from the first or the second. Two crystals. The same is true for photon B and photon D.

　　The phase shifter can change the phase of the photon. If a phase shifter is placed between two crystals and the degree of phase shifting is constantly changed, it will cause constructive or destructive interference at the detector. Assuming that each crystal can produce 1000 pairs of photons per second; when producing constructive interference, the detector can receive 4000 pairs of photons per second; when producing destructive interference, the number of photons received is zero, because although a single crystal The number of photons generated per second is 1000, but the entire system does not generate a single photon.

　　MELVIN's solution also includes such overlapping routes. What puzzled Klein was that there were only two crystals in his algorithm. MELVIN did not use these two crystals at the beginning of the experiment, but put them in an interferometer (the interferometer can divide the travel path of a photon into two and combine the two into one). After spending a lot of research work, he realized that the experimental setup used by MELVIN was equivalent to using more than two crystals, so that a higher-dimensional entangled state could be produced.

　　In addition to generating complex entangled states, the experimental configuration using more than two crystals can also achieve a "generalized" version of Salinger's experiment with two crystals in 1994. Crane’s colleague Everem Steinberg at the University of Toronto was shocked by the results of artificial intelligence research. "As far as I know, this kind of generalization is something that humans can never imagine or achieve by themselves."

　　In one of the generalized experimental configurations, the number of crystals is four, each crystal generates a pair of photons, and there are four overlapping paths to four detectors. Quantum interference can form constructive interference, that is, all four detectors can detect photons; or destructive interference, that is, no detector can detect photons.

　　But until not long ago, it has been a distant dream to actually carry out such an experiment. However, in March this year, researchers from the University of Science and Technology of China and Crane reported in a preprinted paper that they had built a complete experimental configuration on a photonic chip and successfully carried out this experiment. Due to the extremely strong optical stability of the photonic chip, the researchers continuously collected more than 16 hours of data in the experiment, which is impossible to achieve in large-scale experiments.

　　When initially trying to simplify and generalize MELVIN's research results, Klein and his colleagues realized that this solution is actually very similar to an abstract expression in mathematics called "graph". The graph is composed of "vertices" and "edges", which can be used to describe the pairing relationship between objects. In quantum experiments, the path of each photon can be represented by a "vertex", and each crystal can be represented by an "edge" connecting two vertices. MELVIN first created such a graph, and then carried out a series of mathematical operations called "perfect matching", that is, each vertex is connected to only one edge. This process can greatly simplify the calculation of the final quantum state, but it is still difficult for humans to understand.

　　However, the emergence of MELVIN's successor THESEUS changed this. It can filter the complex graph generated in the first step, and gradually reduce the number of edges and vertices to no less (if it is further reduced, the experimental setup will not be able to produce the desired quantum state). Such a graph is much simpler than MELVIN's perfect match graph, so it is easier to interpret by humans.

　　Eric Garvalcandi of Griffith University in Australia was deeply shocked by these research work. "These machine learning techniques are really interesting. To human scientists, some of the solutions look very'novel'. But at this stage, these algorithms are far from being able to come up with new ideas and create new concepts. However, I believe that this day will come sooner or later. Although we are still learning to walk with babies today, the journey of a thousand miles begins with a single step after all."

　　Steinberg agrees with this view. "For now, these are wonderful tools. Like all good tools, they have helped us achieve some things that were impossible to achieve." (Leaf)