"A couple of weeks ago I got a nice surprise from a news story on a physics website headlined "The Experimental Realization of Quantum Overlapping Tomography." It reported on breakthrough work by Zhengning Yang and colleagues at Nanyang Technical University, who implemented a technique suggested by Jordan Cotler and me in 2020. This line of work aims to get a clear image of the notoriously hard-to-view quantum world.
Each of the three words in Quantum Overlapping Tomography (QOT) can use some unpacking to understand what is and why it matters.
Let's look at the Q first. A good quantum picture needs a very large canvas, even when it's depicting something very small. For example, the wave functions for systems of two to five electrons exist in spaces ranging from six to 15 dimensions. This puts physicists in a peculiar situation. We know what the relevant equations are, but using current supercomputers we can only solve them very approximately. If we could do a better job of understanding quantum reality, we would be able to take chemistry and materials science, including the design of drugs and catalysts, to new levels. Wave functions of multi-electron systems contain all the needed information.
Quantum simulators and quantum computers are meant to rise to this challenge.
Ideally, they can embody the complete quantum-mechanical wave function of the system you're hoping to understand, as a sort of scale model. But with that, the problem will only be half-solved. The thing is, it's not easy to read the information that wave functions contain. In quantum mechanics, infamously, measuring a wave function "collapses" it and spoils it for further use.
That's where the T, for tomography, comes in. "Tomography" derives from the Greek "tomos" meaning "slice, or section." It is also the T in CT scan (Computer-assisted Tomography). CT scans assemble the information from many 2-D X-rays into an accurate 3-D rendering of the body's interior. The idea with QOT is to do something similar in the vaster quantum realm.
The problem of reading quantum wave function information is something like the challenge posed by games like Wordle and Mastermind. In those games, you make multiple queries (akin to measurements) and get back only partial information from each one. But now imagine that the Wordle contains thousands of characters or the Mastermind template thousands of pegs and dozens of colors.
That brings us to the other letter, O for overlapping. A good strategy for the quantum measurement problem is making measurements that sample the wave function with different resolutions. This gives you overlapping images that you can weave together into a fuller picture. The Nanyang researchers tested the algorithms that Dr. Cotler and I came up with by showing that they gave back a complicated test image accurately and efficiently.
The good news from the Nanyang experiment brought back pleasant memories of the long summer walk by the Baltic Sea, outside Stockholm, that Dr. Cotler and I took a few years ago.
There, responding to a challenge from the brilliant Chinese physicist Jian-Wei Pan, we cracked the problem of making wave function measurement reasonably practical.
The news came just as I was recovering from gallbladder surgery. That was weirdly poetic, since it was a CT scan that had nailed my diagnosis. That technology has taken a lot of the guesswork out of surgery.
Quantum technology will eventually do the same for biochemistry. Eventually, by supplying potent new medicines, it might even take the surgery out of treatment." [1]
1. REVIEW --- Wilczek's Universe: A New Way To See the Quantum World
Wilczek, Frank. Wall Street Journal, Eastern edition; New York, N.Y. [New York, N.Y]. 18 Mar 2023: C.4.
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