Microscopic analogs of the Greenberger-Horne-Zeilinger experiment on an NMR quantum computer

A scheme is proposed to implement microscopic analogs of the Greenberger-Ho rne-Zeilinger experiment, as described by Lloyd, on a nuclear magnetic reso nance (NMR) quantum computer. This scheme includes how to prepare the effec tive pure spin state \0000] (a state with all the spins pointing along the direction of the magnetic field) from a state at thermal equilibrium, how t o transform it into states of the form, e.g., (\000) -\111])\0) (which comp rises the first three spins in an entangled state and the fourth register-s pin), and how to measure the eigenvalue of the operator product like sigma( x)(1)sigma(y)(2)sigma(y)(3) for such three-spin entangled states, where sig ma(i) is the Pauli matrix for the ith spin, and store the result on the fou rth spin. Also proposed is a general method to implement the controlled-not gate, an essential gate for any quantum algorithm, on n-qubit NMR quantum computers with n greater than or equal to 4. [S1050-2947(99)01209-3].