State injection, lattice surgery, and dense packing of the deformation-based surface code

Resource consumption of the conventional surface code is expensive, in part due to the need to separate the defects that create the logical qubit far apart on the physical qubit lattice. We propose that instantiating the deformation-based surface code using superstabilizers will make it possible to detect short error chains connecting the superstabilizers, allowing us to place logical qubits close together. Additionally, we demonstrate the process of conversion from the defect-based surface code, which works as arbitrary state injection, and a lattice-surgery-like controlled not (cnot) gate implementation that requires fewer physical qubits than the braiding cnot gate. Finally, we propose a placement design for the deformation-based surface code and analyze its resource consumption; large-scale quantum computation requires 25d2+170d+2894 physical qubits per logical qubit, where d is the code distance of the standard surface code, whereas the planar code requires 16d2-16d+4 physical qubits per logical qubit, for a reduction of about 50%.