[Colloquium] Tushant Mittal MS Presentation/Nov 12, 2021

[Megan Woodward]

This is an announcement of Tushant Mittal's MS Presentation.
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Candidate: Tushant Mittal

Date: Friday, November 12, 2021

Time: 2 pm CST

Remote Location:  https://uchicago.zoom.us/j/96010336255?pwd=T0xCSzh1Y1RQZ1R4L1JEdzlWc21sQT09<https://urldefense.com/v3/__https://www.google.com/url?q=https:**Auchicago.zoom.us*j*96010336255*pwd*3DT0xCSzh1Y1RQZ1R4L1JEdzlWc21sQT09&sa=D&source=calendar&ust=1635885994819089&usg=AOvVaw35QXdU7zU3eS1mO6uPUxMN__;Ly8vLz8l!!BpyFHLRN4TMTrA!v4DcMXcR4Wg5n3Qn4ckGxtQttcEae-LEildPTvREczXdEcZUbhhgcAXwXuxnIyP_TaD3qx8z$>

Title: Quantum LDPC codes: An exposition of recent product constructions

Abstract: LDPC CSS codes is a class of quantum error correcting codes, and a highly sought-after goal is to construct such codes with distance as close to the number of qubits, N, as possible.

Until recently, the largest distance was slightly better than [\sqrt{N}]  but this has been improved significantly by many constructions based on tensor product and its modifications. In 2020, Evra, Kaufman and Zemor constructed codes of distance [\sqrt{N \log N}]  using tensor products. This was improved by Kaufman and Tessler to  [\sqrt{N} \log^k N]  for any . Hastings, Haah and O'Donnell gave a construction based on a "twisted tensor product" which achieved a distance [N^{3/5}/\mathrm{polylog}(N)] . Panteleev and Kalachev defined a "lifted product'' leading to an almost linear distance of [N/\log N] . Breuckmann and Eberhardt unified and generalized these constructions by providing an abstract framework.

In this talk, we will survey these results focusing primarily on the property of distance. We will also briefly discuss connections to other areas and related open problems. The talk will be introductory and self-contained and no background in quantum computation is assumed (or needed).

Advisors: Janos Simon and Madhur Tulsiani
Committee Members: Janos Simon, Madhur Tulsiani, and Bill Fefferman
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