  An important problem in quantum information is the practical demonstration of
non-classical long-range order on quantum computers. One of the best known
examples of a quantum system with non-classical long-range order is a
superconductor. Here we achieve Cooper pairing of qubits on a quantum computer
to represent superconducting or superfluid states. 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 towards more complex modeling of
superconductivity and superfluidity as well as other phenomena with significant
quantum long-range order on quantum computers.

Quantum Physics;Chemical Physics;Computational Physics