# IQI Weekly Seminar

*,*Graduate Student

*,*Duke University

*,*

**Abstract**: Quantum technologies are maturing by the day and small quantum computers are becoming generally programmable. While hardware quality is constantly improving, quantum error correction remains vital for truly scalable, reliable, and universal quantum computing. Since fully fault-tolerant quantum computing still requires a large amount of overhead, there is a lot of interest in near-term applications with a potential quantum advantage. In this talk, I will first describe a systematic approach that we are pursuing to synthesize logical operators for *arbitrary* stabilizer codes, which is a fundamental task for coded quantum computation. The main tools we utilize are the binary symplectic framework for Clifford gates and our recently proposed extension to integer symplectic matrices for a large set of diagonal gates. Using our methods, I will describe a surprisingly new *classical* coding problem that is intimately related to synthesizing certain logical non-Clifford gates. This connection allows us to argue about the optimality of CSS codes for T gates, which has been an open question in quantum error correction. In the other part of the talk, I will describe our analysis of a belief-propagation algorithm that passes *quantum* messages to decode binary linear codes on a certain classical-quantum channel. The algorithm was proposed by Joseph Renes in https://arxiv.org/abs/1607.04833. This is inspired by deep-space optical communications, where I will show that the algorithm points to a potentially near-term application with a quantum *communication* advantage.

The logical operator synthesis work is based on the following papers: https://arxiv.org/abs/1907.00310, https://arxiv.org/abs/1902.04022, https://arxiv.org/abs/1910.09333, and the last paper was presented at QIP 2020 as a contributed talk. A shorter version of this work is available at https://arxiv.org/abs/2001.04887. The belief-propagation project is joint work with Saikat Guha and Kaushik Seshadreesan at University of Arizona, Tucson, and my co-advisor Henry Pfister. The paper should be posted on the arXiv very soon.