Gil Kalai opened the final morning of plenary speeches at the 2018 International Mathematics Congress today presenting the audience with two related problems, tackling computerized vote-counting systems and quantum computing possibilities.  The talk, he told the audience, would consist of “two puzzles, four parts, six theorems and eight models”.


“My first question is how to find election voting systems that are not full of errors in counting votes,” he said.  A good example, according to the Israeli mathematician, could be seen in the 2016 US presidential elections, where predictions on the outcome were famously off-mark.


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After moving through problems with electronic vote-counting systems for both two- and three-party scenarios using Boolean functions, the professor moved his second question as to whether “quantum supremacy is real, and how it can be realized.”  He outlined Boolean circuits’ applications in computing and quantum computing, Boson sampling and NISQ system sensitivity.


Kalai is Yale’s adjunct professor of mathematics and computer science and Noskwith Professor of Mathematics at the Hebrew University of Jerusalem. His research arguments suggest that constructing the quantum codes necessary for quantum computation is not possible, demonstrating that quantum computational superiority in other quantum systems will also be impossible.


He said that ‘noise’ or errors in the process will affect the outcome of the process.  It will be possible to counteract the possibility that a qubit will become corrupted by noise when quantum computing executes an action, he opined.


“Understanding quantum systems and potentially even the failure of quantum computers is related to the fascinating mathematics of noise stability and noise sensitivity, and its connections to the theory of computing,” the professor concluded in his presentation. “Exploring this avenue may have important implications to various areas of quantum physics.”


Although Kalai’s research on quantum computing and its obstacles has been somewhat controversial, provoking complaints from mathematicians with opposing views, he remains one of his discipline’s much-decorated academics. Most recently, Kalai won the 2012 Rothschild Prize in Mathematics, in addition to winning the Pólya Prize, Erdos Prize and Fulkerson Prize earlier in his academic trajectory.


The mathematician’s enthusiasm for ICM shone through as he concluded his plenary.  He praised Brazilian mathematics on display throughout the nine-day event as “excellent, passionate and diverse” and said he hopes to be around to see solutions to quantum computing’s noise problems at future ICM meetings.