Fault-tolerant logical state preparation on static 2D atom arrays.

Recent experimental demonstrations have shown the realization of logical operations between encoded qubits using reconfigurable atom arrays, where non-local connectivity is engineered by the coherent transport of atoms across two spatial dimensions. While reconfigurable arrays offer great potential for connectivity within larger quantum registers, it is not yet clear whether the excess heating and atom loss during movement are more beneficial or detrimental to the state preparation fidelity of small-distance logical qubits than the constraints associated with using just local connectivity with nearest-neighbors interactions. Furthermore, alternatives such as teleportation of entangling gates can also be used to create long-range interactions across large-scale quantum registers based on static traps with limited local connectivity. For systems featuring both static and dynamic traps, it is worth investigating whether a hybrid transport solution would be more optimal for achieving fault-tolerant computation.

Here, we evaluate the performance of different fault-tolerant encodings and fault-tolerant parity-check measurement circuits for the distance-3 color code ([[7,1,3]] code) mapped to a 2D square lattice with limited local connectivity. We demonstrate how fault-tolerant designs for the level-1 encoding (7-qubit logical state) can be accomplished using two-qubit gates between nearest-neighbor qubits, mid-measurements, and post-selection. Additionally, we illustrate how fault-tolerant transport can be implemented in a static array using SWAP and CNOT gate teleportation to perform logical gates between encoded qubits and to prepare larger logical states.