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

Abstract

We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magneticresonance ͑NMR͒ two-qubit quadrupole system, 23 Na ͑spin 3/2͒ 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 Ϸ70% and Ϸ100%, 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 T 2 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.

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

“…Internal molecular or atomic motions induce random fluctuations in the EFG at the position of the nucleus, which produce spin relaxation [40,41]. In the QIP context, the random fluctuations can be seen as a source of noise, which causes decoherence and energy dissipation, being mapped by proper nonunitary operators [24].…”

Quantum information processing through nuclear magnetic resonance

“…More information about the sample preparation and experimental procedures can be found in references [1], [2], [25] and [26].…”

“…Therefore, it is important to investigate relaxation in the context of NMR quantum computing. References [26] and [27] reports a spinlattice relaxation study of various NMR quantum computing coherent states.…”

Quantum State Tomography and Quantum Logical Operations in a Three Qubits NMR Quadrupolar System

“…Nuclear magnetic resonance (NMR) has provided unique methods for demonstrating the realization of quantum logical operations and characterizing the quantum state of spin systems. The great sucess achieved so far by NMR QC is related to its ability for controlling the dynamics of the spins through radio frequency (RF) pulses [6,7]. This great control also enables the creation of pulse sequences for the determination of elements of the nuclear spins density matrix, called the Quantum State Tomography process (QST).…”