  We propose and experimentally realize an algorithmic benchmark that
demonstrates coherent control with a sequence of quantum operations that first
generates and then decodes the cat state (|000...>+|111...>)/sqrt(2) to the
standard initial state |000...>. This is the first high fidelity experimental
quantum algorithm on the currently largest physical quantum register, which has
seven quantum bits (qubits) provided by the nuclei of crotonic acid. The
experiment has the additional benefit of verifying a seven coherence in a
generic system of coupled spins. Our implementation combines numerous nuclear
magnetic resonance (NMR) techniques in one experiment and introduces practical
methods for translating quantum networks to control operations. The
experimental procedure can be used as a reliable and efficient method for
creating a standard pseudo-pure state, the first step for implementing
traditional quantum algorithms in liquid state NMR. The benchmark and the
techniques can be adapted for use on other proposed quantum devices.
