Title: Two-dimensional implementations of quantum LDPC codes.
Abstract: Quantum LDPC codes are promising to reduce the cost of
quantum error correction but can they really be implemented with
current quantum hardware which typically look like a 2D grid of
qubits equipped with local gates? In this talk we will provide two
answers to this question. First we will discuss obstructions to local
implementation of quantum LDPC codes which suggest that quantum
LDPC are impractical with 2D local quantum hardware. Second, we
propose an implementation of quantum LDPC codes based on long-range
connections. With this design, we obtain a threshold of 0.28% for a family
of quantum LDPC codes using 49 physical qubits per logical qubit. For a
physical error rate of 10^-4, this family reaches a logical error rate of 10^-15
using fourteen times fewer physical qubits than the surface code.
Joint work with Michael Beverland and Maxime Tremblay.
Ref: arXiv:2109.14599 and arXiv:2109.14609
