Fig. 2: Code layout, logical operators, and boundary conditions.
From: High-rate quantum LDPC codes for long-range-connected neutral atom registers
a Classical polynomial seeds constraining stabilizer shape and ruling one lattice direction each. Both symmetric and asymmetric configurations are allowed. The examples here refer to the cases n1 = 6, k1 = 2 (vertical) and n2 = 15, k2 = 7 (horizontal). Data(ancilla) qubits are colored black(white). b The [[65, 9, 4]] k = 3-LDPC code with the 9 partially overlapping horizontal logical Z operators shown in different colors. c Array shape and two stabilizers with periodic boundary conditions (PBC), open boundary conditions (OBC), and squeezed open boundary conditions, assuming n = 7 and k = 3 (equal seeds). Long-range gates of boundary stabilizers are effectively shorter upon array reshaping (from length j = 5 lattice sites to j = 4 or j = 3 here), which should be included in quantum error correction simulations under a range-dependent noise model.
