Same quantum state means the electrons have a wide range of energies in the material. In the superconducting state, the electron pairs act as a single bosonic particle — they do not obey the Pauli Exclusion Principle and can all exist in the same, very low, energy state.
This enables the Cooper pairs to interact with the vibrations (phonons) of the crystal lattice in such a way that they can pass through the lattice without giving or taking energy from the lattice atoms, which reduces the resistance to zero.
Having no resistance in the windings of the electromagnets enables the flow of the large currents necessary to create very strong magnetic fields, needed to maintain the radius of curvature of particles moving close to the speed of light.