# The physical limit of quantum optics resolves a mystery of computational complexity

Credit: ©Science China Press

Linear optics represents one of the best examples for demonstrating quantum physics. It works at room temperatures, and can be observed with relatively simple devices. In linear optics, one studies physical processes that conserve the total number of photons. In the ideal case, if there are 100 photons at the beginning, no matter how complicated the physical process is, there will be exactly 100 photons left in the end.

Photons are bosonic non-interacting particles. However, they can still interference with each other, exhibiting non-trivial quantum effects. A typical example is the Hong-Ou-Mandel experiment, where two identical photons are sent to an experimental device. After a simple linear transformation, the two photons become as if they are stuck together and unwilling to separate. In addition to providing a foundational understanding of quantum mechanics, the study of linear optics also leads to various applications in different areas of science.

In recent years, the unqiue properties of linear optical systems have also inspired the development of computational complexity theory. In 2012, Professor Scott Aaronson at MIT (currently at The University of Texas at Austin) proposed a linear optical method for demonstrating the quantum (computational) supremacy, which is based on the concept of boson sampling. More specifically, Aaronson suggested that for a class of sampling problems based on linear optical systems, it would be impossible in practice to apply any classical computer to simulate. This idea immediately sparks a race for reaching the status of “quantum supremacy”. Many quantum optical laboratories around the world have become interested in developing boson sampling systems, for breaking the records in terms of photon numbers. On the other hand, computer scientists are busy in applying supercomputers to raise the bar for achieving quantum supremacy.

However, in terms of applications, one can hardly apply the model of boson sampling to solve practical problems. Therefore, Aaronson raised an open question in 2012: apart from sampling problems, can one exploit linear optics to achieve quantum supremacy in terms of decision problems with a YES/NO answer? Recently, Prof. Man-Hong Yung, associate professor of SUSTech and his colleagues published a paper “Universal bound on sampling bosons in linear optics and its computational implications”, in *National Science Review* (*NSR*), offering a complete solution to the open problem posed by Aaronson.

Specifically, Yung’s team uncovered a fundamental limit on the transition probabilities of linear optical systems, constraining the ability to transfer bosons using linear optical devices. Together with the tools of quantum optics, they developed a classical algorithm that can efficiently estimate the transition amplitude with a bounded error. Consequently, these results lead to a negative answer to Aaronson’s open problem. In other words, for encoding hard decision problems, one would need to make use of more complicated quantum optics systems, instead of just linear optics.

As an interdisciplinary domain between quantum physics and computer science, quantum information science remains to be a highly-active research area. On one hand, the results of Yung’s team contribute to the theoretical foundation of quantum optics; on the other hand, in addition to boson sampling, these results point to a novel perspective on computational complexity problems in terms of quantum optics. Undoubtedly, in the future, we should expect to see many more exciting results like these in this area.

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See the article:

Man-Hong Yung, Xun Gao, Joonsuk Huh

Universal bound on sampling bosons in linear optics and its computational implications

*Natl Sci Rev* (April 2019) doi: 10.1093/nsr/nwz048

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**Media Contact**

Man-Hong Yung

yung@sustc.edu.cn

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