Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm

Abstract

Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-1 2 nuclei of a molecule, is well established. Nuclei with spinϾ1/2 oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-3 2 ͑2 qubit͒ system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-1 2 nuclei, the gate time decreases, increasing the clock speed of the quantum computer.

Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance

“…Among these, nuclear magnetic resonance (NMR) has shown great promise by demonstrating several quantum algorithms and other QIP tasks on small-scale devices. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The last step in any quantum information processing task is the "readout" of the output.…”

Writing Electronic Ferromagnetic States in a High-Temperature Paramagnetic Nuclear Spin System

“…This system can be used to emulate any two-qubit quantum system [16,[20][21][22][23]. In NMR systems the Zeeman energy levels are very small if compared to the thermal energy at room temperature.…”

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

“…This method was later adapted for homonuclear coupled spins 1/2 [10,11] and also for quadrupolar spin 3/2 systems [12][13][14][15][16][17], where nonselective pulses were replaced by transitionselective RF pulses. The disadvantage of such method is the long time required to perform a selective pulse, producing considerable unwanted evolution of the system during the QST process.…”