IQIM Postdoctoral and Graduate Student Seminar

Joint AWS/IQIM Seminar

Abstract: Seminal results by Bravyi, Poulin and Terhal have shown that quantum codes are limited by locality. As a consequence, all topological codes witness sharp tradeoffs between their rate and distance. Quantum LDPC codes can be viewed as a generalization of topological codes constructed using spatially-nonlocal connections. It is unclear what, if any, fundamental constraints these codes obey. The state-of-the-art code parameters are far from what their classical counterparts can achieve. We explore this question and present no-go results that shed some light on what is not possible. We approach this question in two ways, using abstract and physical constraints. First, we use a graph-theoretic representation of a quantum code to show that the connectivity of this representation allows us to understand limitations of the associated code. We obtain generalizations of the Bravyi-Poulin-Terhal and Bravyi-Koenig bounds. We then study the complementary problem of embedding a code in D Euclidean dimensions. We ask how many long-range interactions we need to obtain a target code dimension k and distance d. Focusing on 2 dimensions (and ignoring polylogarthmic corrections), we find that a code with distance d requires Ω(d) interactions of length Ω(d/√n). Furthermore, a constant-rate code distance d requires Ω(n) interactions of length Ω(√d). This is joint work with Nouédyn Baspin. It is based on the papers arXiv: 2106.00765 and arXiv: 2109.10982

Attend by zoom at https://caltech.zoom.us/j/81483492264