Quantum Theory, Control Theory, and Quantum Control.

Naoki Yamamoto (Associate Professor, Department of Applied Physics and Physico-Informatics)

When you hear the term quantum mechanics, I think the first thing that comes to mind is the "uncertainty relation." This is the idea that when you "look" at a quantum object, you gain information, but the observation itself affects the object, increasing a certain kind of "uncertainty." For example, recent technology makes it possible to capture individual atoms, but looking at them—that is, shining light on them—causes that light to move the atoms randomly. I apologize for the vague explanation, but in any case, the point is that there are matters in quantum theory that are "absolutely indeterminable." The laws of physics in our everyday world, when pursued to their limits, reach a level where everything is "definitely determinable." It is possible to observe a flying ball without affecting it at all. In principle, you could obtain all information about the ball's direction, speed, rotation, and everything else in real time and with perfect accuracy. In that case, you could predict the ball's trajectory with 100% accuracy. In quantum mechanics, however, no matter how ideal the conditions, it is impossible to make an observation that does not affect the object at all.

Now, let's talk about "control." This concept of control is deeply involved in our daily lives. We can drive a car because we are constantly observing our ever-changing surroundings and adjusting the steering wheel and accelerator accordingly. You can't drive blindfolded. The reason the air conditioning in a room is kept constant is also thanks to control. A sensor continuously monitors the room's temperature and adjusts the air conditioning based on that information. These are all examples of what is called "feedback control." In other words, you observe an object, obtain information, and then apply an operation to the object based on that information.

Feedback control is powerful. As in the examples above, in the natural, uncontrolled world, a room with constant air conditioning does not exist. In other words, feedback control can create situations that could not exist in a natural state. So, wouldn't it be wonderful if we could apply feedback control to a quantum system? However, as mentioned earlier, when you "look" at a quantum system, you must pay the price of inevitably having an uncertain effect on the object. This makes it a very tricky subject to control. Is it possible to observe a quantum system, pay the price of increased uncertainty, and yet use the information obtained to control it...? In fact, it is possible!!

It is impossible to briefly explain why this is possible or how to achieve it, nor is that the focus of this short article. I would also like to talk about the benefits of feedback control, but I will omit that as it is a bit too technical. However, I will add the fact that its theoretical framework is extremely beautiful and orderly, along with a very simple anecdote. The theory was published in the late 80s, but it was initially a bit too mathematically abstruse, and for more than 10 years, no one could follow it or grasp its true meaning. I myself, having just earned my degree in 2004 and moved to the US as a postdoc, was only using the superficial aspects of this theory in my research. But in that same year, a paper was published that clearly explained the theory. I still remember the thrill I felt when I immediately read that paper thoroughly and was able to understand its true meaning. It was a theoretical framework that fused the essences of physics, mathematics, and engineering—or to be a little more specific, quantum mechanics, probability and stochastic processes, and control and signal processing. Fortunately, the author of that brilliant paper, a Mr. B, was the same age as me, and we came to the US as postdocs at the same university and in the same lab in the same year. We became friends, co-authored papers, I borrowed his name for my child's middle name... It was a very fulfilling and enjoyable postdoc life in America.

I've digressed, but let me say one last thing. I believe that research is ultimately driven by "inspiration" at a personal level. Having been so moved by the system that fused the essences of physics, mathematics, and engineering as described above, I feel that I continue my research in search of similar inspiring experiences. I hope to one day discover or build a beautiful theoretical framework that merges different fields myself.