Towards bivariate bicycle codes with open boundary conditions

Quantum low-density parity-check codes are a promising route for quantum error correction since they might offer a more resource-efficient alternative to surface code architectures. In particular, bivariate bicycle codes have recently gained attention due to their 2D-local structure, high encoding rate, and promising performance under simulation. In this work, we explore how one can transform bivariate bicycle codes that are defined on lattices with periodic boundary conditions to codes that have the same locality properties on a 2D lattice with open boundary conditions. We explain how this is always possible when the codes are hypergraph products of two classical cyclic codes. For certain examples that are not hypergraph products, we explain how a similar construction works by drawing a connection to 2D color codes.