Featured Speaker :  Zhiyang He (MIT Mathematics)

Title :  Quantum locally testable codes with constant soundness

Abstract :  

A classical code C is testable if the syndrome of a proposed code word w reveals more than whether w belongs to the code: the relative weight of the syndrome is also proportional to the relative distance of w from the codespace, and their ratio is called the soundness of C. The theory of code checking is a widely successful area of the theory of computing, affecting PCP theory, combinatorial optimization, combinatorial property testing, program checking, and even cryptography. 

In this talk, we present constructions for the first few families of quantum locally testable codes (qLTCs) with constant soundness. Constructing qLTCs is an open problem of great interest, due to the recent breakthroughs in qLDPC codes. They also seem closely connected to the quantum PCP conjecture, a major area of research in quantum complexity theory. We will present a few simple constructions that achieve new, exotic parameters, and discuss their differences.