Peter Shor, the professor of applied mathematics at MIT, was named the winner of the 2023 Breakthrough Prize in Fundamental Physics. He shares the $ 3 million prize with three others for “fundamental work in the field of quantum information”: David Deutsch of the University of Oxford, Charles Bennett of IBM Research and Gilles Brassard of the University of Montreal.

In announcing the award, the Breakthrough Prize Foundation highlighted Shor’s contributions to the field of quantum information, including Shor’s eponymous algorithm for factoring extremely large numbers and an algorithm for correcting errors in quantum computers.

“These ideas not only paved the way for today’s rapidly developing quantum computers; now they are also at the frontiers of fundamental physics, particularly in the study of metrology – the science of measurement – and quantum gravity “, reads the announcement of the award.

“I am very grateful to see that the award went to quantum information and quantum computing theory this year,” commented Shor. *MIT News*. “My three co-winners were the most influential people in founding this field. I consider them friends and they all clearly deserve it. “

Additionally, a former MIT alumni, Daniel A. Spielman PhD ’95, won the Breakthrough Prize in Mathematics 2023 for “contributions to theoretical computer science and mathematics, including spectral graph theory, the Kadison-Singer problem, l numerical linear algebra, optimization and code theory.

“I am thrilled to see that both Peter Shor and Dan Spielman have been awarded with the Breakthrough Prizes in Fundamental Physics and Mathematics, respectively,” said Michel Goemans, RSA Professor and head of MIT’s Mathematics Department. “Both would have been natural candidates for the Breakthrough Prize in Theoretical Computer Science, if such an award had existed. Peter and Dan are graduate students of our math department, both have held tenure positions in our department and were members of the theory group at CSAIL, and both have received the same awards. It is a testament to the importance of theoretical computer science in all disciplines, especially mathematics and physics.

**Quantum seeds**

The first seeds of the potential of quantum computing were planted through the first algorithms derived from Deutsch, Bennett, Brassard and Shor.

In the early 1980s, Deutsch began thinking about problems whose solutions could be speeded up using quantum algorithms, derived formulas using the laws of quantum mechanics, rather than classical physics. He was the first to develop a quantum algorithm that could solve a simple, albeit artificial, problem much more efficiently than a classical algorithm.

Meanwhile, Bennett and Brassard were also looking for uses for quantum information. In 1984 they developed the first quantum encryption protocol, BB84. They put forward the idea that two distant parties could agree on a secret encryption key, which would be safe against eavesdroppers, based on a strange quantum principle in which the value of the encryption key would be instantly disturbed and therefore unreadable when measured.

Their work demonstrated the earliest practical application of quantum information theory. It was also Shor’s first introduction to the camp. The mathematician was working at AT&T Bell Labs at the time, and Bennett came over to give a talk on his new quantum key cryptography system. “Their work inspired me to do some reflection and research on quantum information,” recalls Shor. “But I didn’t actually go anywhere at the time.”

A decade later, in 1994, Shor introduced his reference algorithm. Shor’s algorithm describes how a sufficiently large quantum computer could efficiently factor extremely large numbers, a task that would take longer than the age of the universe to solve by the most powerful classical supercomputer.

Most data encryption schemes today rely on the difficulty of factoring to keep information secure. Shor’s algorithm was the first to show that, in theory, a quantum system could break through most modern data security walls. To do this in practice, however, a system of many precisely controlled quantum bits would be required. Even then, scientists assumed that the slightest noise in the environment would disrupt the delicate qubits and trigger a wave of errors in their calculations that could not be corrected without further disturbing the qubits.

“When I first invented this factorization algorithm, people thought it would theoretically stay forever because there was this argument that you couldn’t correct errors on a quantum computer,” says Shor.

Soon after, in 1995, Shor worked out another algorithm, this time on quantum error correction, which showed that errors in a quantum system could indeed be isolated and corrected without disturbing the qubit itself, thus leaving quantum computing intact. The vision of a practical quantum computer became immediately tangible.

“With these two bombshell contributions, Peter laid the groundwork for quantum computing to become the huge field it is now,” says Alan Guth, Professor of Physics Victor F. Weisskopf at MIT, who as a former recipient of the Breakthrough Award, was the one who called Shor to break the news of this year’s award.

“It was a real pleasure for me to be able to tell him he’s one of the winners,” says Guth. “His algorithms took the world by surprise and ignited the field of quantum computing. And despite his spectacular contributions, Peter continues to be a warm, friendly and smiling colleague with everyone around him. “

“Peter is a wonderful colleague and he is absolutely unique,” adds Goemans. “His thought process seems to parallel the quantum algorithms he designs and invents: from intertwined ideas and a superposition of states, a brilliant solution often emerges in a Eureka moment!”

“One of the best things about MIT is that we have great students,” says Shor, who earned a Ph.D. in applied mathematics from MIT in 1985. He then spent a year as a postdoc at the Mathematical Sciences Research Institute before moving on. to work at AT&T Bell Labs, where he developed the Shor algorithm. In 2003 he returned to MIT, where he has continued his research and teaching for the past 20 years.

Today he is working to formulate a quantum information theory, which would describe how data can be stored and transmitted, using the principles of quantum physics. Will there come a day when quantum computers are advanced enough to break through our classic security systems?

“In five to 10 years, we could be at the beginning of a Moore’s law, where quantum computers will steadily improve every few years,” Shor predicts. “I suspect they will improve fast enough that within two or three decades we will have quantum computers capable of doing useful things. Hopefully, when quantum computers are this big, we will use several cryptographic systems that are not susceptible to quantum computers. “

Shor credits his father for promoting his early interest in mathematics. As a boy, he browsed through his father’s problems *American scientist*to find your favorite section.

“Martin Gardner had a column, ‘Mathematical Games,’ which was really amazing,” recalls Shor. “Sometimes it was a conundrum, sometimes an account of a new discovery in mathematics, and often it was at a level that I could understand. I was looking forward to reading it every month, and it was something that turned me into math right from the start. “

**Beautiful discoveries**

Daniel Spielman, winner of this year’s Breakthrough Award in Mathematics, earned a PhD in applied mathematics from MIT in 1995, for which he was recommended by Michael Sipser, Donner Professor of Mathematics and former Dean of the MIT School of Science . Spielman then joined the math department and was a faculty member at MIT until 2005, before moving on to Yale University, where he is currently Sterling Professor of Computer Science, Mathematics, Statistics and Data Science.

Spielman specializes in algorithm design and analysis, many of which have provided insights “not just for mathematics, but for highly practical problems in computer science, signal processing, engineering, and even clinical trial design,” notes the Breakthrough Foundation in their announcement today.

“Dan has made a number of important and beautiful discoveries over the years, from expander-based error correction codes, to smooth algorithm analysis or spectral sparsification of graphs, all of which feature groundbreaking mathematics,” says Goemans.

Among the numerous discoveries, Spielman is best known for solving the Kadison-Singer problem, which for decades was deemed unsolvable. The problem can be interpreted as a fundamental question for quantum physics: in a quantum system, is it possible to decipher new information, if only some of the properties of the system are observed or measured? The answer, most mathematicians agreed, was no.

Over the decades, the Kadison-Singer problem has been reformulated and shown to be equivalent to problems in a wide range of mathematical fields. And in 2013, Spielman and his colleagues solved one of these equivalent formulations involving linear algebra and matrices, showing that the answer was yes: in fact, it was possible to determine the sum of a quantum system from its parts.

The Breakthrough Prizes are a series of international awards that recognize scientists’ achievements in three categories: fundamental physics, mathematics and life sciences. The awards were founded by Sergey Brin; Priscilla Chan and Mark Zuckerberg; Julia and Yuri Milner; and Anne Wojcicki, and were sponsored by foundations established by them. The 2023 awards will be presented during a gala awards ceremony and the winners will take part in conferences and discussions.

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