Speaker: Yu-An Chen (Peking)
Title: Low-overhead fault-tolerant topological quantum memories
Abstract: Quantum error correction is a key ingredient in fault-tolerant quantum computation, protecting quantum information against physical errors. The surface code is a leading architecture because of its locality and high error threshold, but its large qubit overhead remains a major challenge. In this talk, I will present a series of low-overhead topological quantum memories based on bivariate bicycle (BB) codes and their generalizations.
The central idea is to use topological order to guide the design of quantum low-density parity-check (qLDPC) codes. I will show how Laurent-polynomial and Gröbner-basis methods reveal the anyon content of these codes, determine the number of logical qubits, and help optimize code layouts on twisted tori. This viewpoint also leads to planar qLDPC codes with open boundaries, where boundary anyon condensation and lattice grafting reduce qubit overhead while retaining favorable locality and error-correcting properties. I will then discuss self-dual BB codes that support transversal Clifford gates, as well as subsystem BB codes that retain the logical structure of BB codes while enabling local weight-4 gauge measurements.
Together, these constructions highlight topological order as a practical design principle for quantum error correction and suggest a route toward hardware-compatible, low-overhead quantum memories beyond the surface-code paradigm.