| Lightning Talks | |||
| Sr. No | Name | Title | Abstract |
| 1 | Amolak Ratan Kalra | Quantum Circuit Synthesis | In this talk I will attempt to give a broad overview of the connection between quantum circuit synthesis and Bruhat-Tits buildings. I will try to explain how one can translate the problem of finding short quantum circuits for some unitary operator into a question about expansion properties of particular Bruhat-Tits buildings. In particular we study the problem for qutrit gate synthesis .
This is part of work in progress with Mark Deaconu, Nihar Prakash Gargava, Michele Mosca and Jon Yard. The project relies on and is greatly informed by earlier seminal works of Peter Sarnak, Shai Evra and Ori Parzanchevski [1-2]. References: [1] Parzanchevski, Ori, and Peter Sarnak. "Super-golden-gates for PU (2)." Advances in Mathematics 327 (2018): 869-901. [2] Evra, Shai, and Ori Parzanchevski. "Arithmeticity and covering rate of the 9-cyclotomic Clifford+ D gates in PU (3)." arXiv preprint arXiv:2401.16120 (2024). |
| 2 | Rohit Yadav | Majority logic decoding of affine Grassmann codes. | In this talk, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with respect to a fixed coordinate. By leveraging the automorphism groups of these codes, we generate a set of orthogonal parity checks for each coordinate. Using these parity checks, we perform majority logic decoding to correct a large number of errors in affine Grassmann codes. This is a joint work with Prasant Singh and Fernando Pinero. |
| 3 | Ashutosh Shankar | Algorithmizing the Multiplicity Schwartz-Zippel Lemma | The multiplicity Schwartz-Zippel (MSZ) lemma asserts that over a field, a low-degree polynomial cannot vanish with high multiplicity very often on a sufficiently large product set. Since its discovery in a work of Dvir, Kopparty, Saraf and Sudan [SIAM J. Comput., 2013], it has found numerous applications; in particular, in the definition and properties of multiplicity codes by Kopparty, Saraf and Yekhanin [J. ACM, 2014]. In this work, we show how to algorithmize the MSZ lemma for arbitrary product sets over any field. In other words, we give an efficient algorithm for unique decoding of multivariate multiplicity codes from half their minimum distance on arbitrary product sets over all fields. Our algorithm builds upon a result of Kim and Kopparty [ToC, 2017] who gave an algorithmic version of the SZ lemma (without multiplicities) or equivalently, an efficient algorithm for unique decoding of Reed-Muller codes over arbitrary sets. |