Quantum-information processing by nuclear magnetic resonance: Experimental implementation of half-adder and subtractor operations using an oriented spin-7/2 system

The advantages of using quantum systems for performing many computational tasks have already been established. Several quantum algorithms have been developed which exploit the inherent property of quantum systems such as superposition of states and entanglement for efficiently performing certain tasks. The experimental implementation has been achieved on many quantum systems, of which nuclear magnetic resonance has shown the largest progress in terms of number of qubits. This paper describes the use of a spin-7/2 as a three-qubit system and experimentally implements the half-adder and subtractor operations. The required qubits are realized by partially orienting ${}^{133}\mathrm{Cs}$ nuclei in a liquid-crystalline medium, yielding a quadrupolar split well-resolved septet. Another feature of this paper is the proposal that labeling of quantum states of system can be suitably chosen to increase the efficiency of a computational task.