Relaxation of coherent states in a two-qubit NMR quadrupole system

We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system, ²³Na (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum “reading” operators and comparing the recovered state with the original one. The degree of recovery varies between ≈70% and ≈100%, depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant T₂ is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.