# Gil Kalai

**Gil Kalai** (born 1955) is the Henry and Manya Noskwith Professor of Mathematics at the Hebrew University of Jerusalem, and adjunct professor of mathematics and of computer science at Yale University.[1]

Gil Kalai | |
---|---|

Born | 1955 |

Alma mater | Hebrew University (PhD) |

Scientific career | |

Fields | Mathematics |

Institutions | Hebrew University of Jerusalem Yale University |

## Biography

Gil Kalai received his Ph.D. from Hebrew University in 1983, under the supervision of Micha Perles,[2] and joined the Hebrew University faculty in 1985 after a postdoctoral fellowship at the Massachusetts Institute of Technology.[3] He was the recipient of the Pólya Prize in 1992, the Erdős Prize of the Israel Mathematical Society in 1993, and the Fulkerson Prize in 1994.[1] He is known for finding variants of the simplex algorithm in linear programming that can be proven to run in subexponential time,[4] for showing that every monotone property of graphs has a sharp phase transition,[5] for solving Borsuk's problem (known as Borsuk's conjecture) on the number of pieces needed to partition convex sets into subsets of smaller diameter,[6] and for his work on the Hirsch conjecture on the diameter of convex polytopes and in polyhedral combinatorics more generally.[7]

He was the winner of the 2012 Rothschild Prize in mathematics.[8] From 1995 to 2001, he was the Editor-in-Chief of the Israel Journal of Mathematics. In 2016, he was elected honorary member of the Hungarian Academy of Sciences.[9] In 2018 he was a plenary speaker with talk *Noise Stability, Noise Sensitivity and the Quantum Computer Puzzle* at the International Congress of Mathematicians in Rio de Janeiro.

## Kalai's conjectures on quantum computing

**Conjecture 1 (No quantum error correction)**. The process for creating a quantum error-correcting code will necessarily lead to a mixture of the desired codewords with undesired codewords. The probability of the undesired codewords is uniformly bounded away from zero. (In every implementation of quantum error-correcting codes with one encoded qubit, the probability of not getting the intended qubit is at least some δ > 0, independently of the number of qubits used for encoding.)

**Conjecture 2**. A noisy quantum computer is subject to noise in which information leaks for two substantially entangled qubits have a substantial positive correlation.

**Conjecture 3**. In any quantum computer at a highly entangled state there will be a strong effect of error-synchronization.

**Conjecture 4**. Noisy quantum processes are subject to detrimental noise.[10]

## References

- Profile at Yale CS department.
- Gil Kalai at the Mathematics Genealogy Project.
- Profile at the Technical University of Eindhoven as an instructor of a minicourse on polyhedral combinatorics.
- Kalai, Gil (1992), "A subexponential randomized simplex algorithm",
*Proc. 24th ACM Symp. Theory of Computing (STOC 1992)*, pp. 475–482. - Friedgut, Ehud; Kalai, Gil (1996), "Every monotone graph property has a sharp threshold",
*Proceedings of the American Mathematical Society*,**124**: 2993–3002, doi:10.1090/S0002-9939-96-03732-X. - Kahn, Jeff; Kalai, Gil (1993), "A counterexample to Borsuk's conjecture",
*Bulletin of the American Mathematical Society*,**29**: 60–62, arXiv:math.MG/9307229, doi:10.1090/S0273-0979-1993-00398-7. - Kalai, Gil; Kleitman, Daniel J. (1992), "A quasi-polynomial bound for the diameter of graphs of polyhedra",
*Bulletin of the American Mathematical Society*,**26**: 315–316, arXiv:math/9204233, doi:10.1090/S0273-0979-1992-00285-9. - Yad Hanadiv, Rothschild Prize.
- "A Magyar Tudományos Akadémia újonnan megválasztott tagjai (The newly elected members of the Hungarian Academy of Sciences)".
*Magyar Tudományos Akadémia (mta.hu)*. 2 May 2016. -
*How Quantum Computers Fail*by Gil Kalai (2011)

## External links

Wikimedia Commons has media related to .Gil Kalai (mathematician) |

- Kalai's home page at Hebrew University
- Combinatorics and more, Kalai's blog
- "Noise stability, noise sensitivity and the quantum computer puzzle - Gil Kalai - ICM2018".
*YouTube*. 19 September 2018. (Plenary Lecture 19)