Quantum LDPC Error Correcting Codes for use on 1D Quantum Dot Arrays

Building upon recent advancements that have demonstrated the shuttling of qubits through a quantum dot array with high fidelity, we conceive of a complete error correction architecture, consisting merely of two parallel quantum dot arrays. One of those two arrays is allowed to "shift" left and right, with different positions allowing for different connectivity between the qubits within the quantum computer. We devise a suite of heuristic methods for compiling any ECC circuit to run with an approximately minimal number of "shifts" of the array. Through simulation we find that fault tolerance can be achieved on several contemporary quantum error correcting codes using only modestly-optimistic noise parameters and the compilation techniques we propose here.