  We propose a polynomial-time algorithm for simulation of the class of pairing
Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The
algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap
between ground and first excited states, and provides a test of the
applicability of the BCS Hamiltonian to mesoscopic superconducting systems,
such as ultra-small metallic grains.

Quantum Physics;Superconductivity