An important problem in quantum information is the practical demonstration of nonclassical long-range order on quantum computers. One of the best known examples of a quantum system with nonclassical long-range order is a superconductor. Here we achieve Cooper-like pairing of qubits on a quantum computer, which can be interpreted as superconducting or superfluid states via a Jordan-Wigner mapping. We rigorously confirm the quantum long-range order by measuring the large $O(N)$ eigenvalue of the two-electron reduced density matrix. The demonstration of maximal quantum long-range order is an important step toward more complex modeling of phenomena with significant quantum long-range order on quantum computers such as superconductivity and superfluidity.