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Preparation of subspace effective-pure state for NMR QIP by means of strongly modulating pulses

Zhou Xian-yi

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

An alternative method for preparing an effective-pure state in a subsystem of a three-spin system for quantum information processing(QIP) in liquid-state nuclear magnetic resonance(NMR) was demonstrated experimentally.With the aid of numerical search methods,strongly modulating pulses(SMP) scheme was obtained and can perform accurate,arbitrary,selective gates on a three-qubit system.Compared with low-power(nuclear-selective) pulse scheme,the number of shaped pulses and the width of each pulse were both reduced.A pair of two-qubit subspace effective-pure states within a three-spin system was acquired simultaneously.The tomography for the spin system agreed with theoretical predictions,which shows that the experiments were successfully implemented.The short pulse-width of SMP substantially reduced the effects of relaxation within the period of pulse.This is very useful for NMR QIP involving larger numbers of qubits.

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An alternative method for preparing an effective-pure state in a subsystem of a three-spin system for quantum information processing(QIP) in liquid-state nuclear magnetic resonance(NMR) was demonstrated experimentally.With the aid of numerical search methods,strongly modulating pulses(SMP) scheme was obtained and can perform accurate,arbitrary,selective gates on a three-qubit system.Compared with low-power(nuclear-selective) pulse scheme,the number of shaped pulses and the width of each pulse were both reduced.A pair of two-qubit subspace effective-pure states within a three-spin system was acquired simultaneously.The tomography for the spin system agreed with theoretical predictions,which shows that the experiments were successfully implemented.The short pulse-width of SMP substantially reduced the effects of relaxation within the period of pulse.This is very useful for NMR QIP involving larger numbers of qubits.
The enormous theoretical potential of Quantum Information Processing (QIP) is driving the pursuit for its practical realization by various physical techniques. Currently Nuclear Magnetic Resonance (NMR) has been the forerunner by demonstrating a majority of quantum algorithms. In NMR, spin systems consisting of coupled nuclear spins are utilized as qubits. In order to carry out QIP, a spin system has to meet two major requirements: (i) qubit addressability and (ii) mutual coupling among the qubits. It has been demonstrated that the magnitude of the mutual coupling among qubits can be increased by orienting the spin-systems in a liquid crystal matrix and utilizing the residual dipolar couplings. While utilizing residual dipolar couplings may be useful to increase the number of qubits, nuclei of same species (homonuclei) might become strongly coupled. In strongly coupled spin-systems, spins loose their individual identity of being qubits. We propose that even such strongly coupled spin-systems can be used for QIP and the qubit-manipulation can be achieved by transition-selective pulses. We demonstrate experimental preparation of pseudopure states, creation of maximally entangled states, implementation logic gates and implementation of Deutsch-Jozsa (DJ) algorithm in strongly coupled 2,3 and 4 spin systems. The energy levels of the strongly coupled 3 and 4 spin systems were obtained by using a Z-COSY experiment.
A new method of preparing the pseudo-pure state of a spin system for quantum computation in liquid nuclear magnetic resonance (NMR) was put forward and demonstrated experimentally. Applying appropriately connected line-selective pulses simultaneously and a field gradient pulse techniques we acquired straightforwardly all pseudo-pure states for two qubits in a single experiment much efficiently. The signal intensity with the pseudo-pure state prepared in this way is the same as that of temporal averaging. Our method is suitable for the system with arbitrary numbers of qubits. As an example of application, a highly structured search algorithm—-Hogg’s algorithm was also performed on the pseudo-pure state | 00 〉 prepared by our method.
We describe a method for improving coherent control through the use of detailed knowledge of the system’s Hamiltonian. Precise unitary transformations were obtained by strongly modulating the system’s dynamics to average out unwanted evolution. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on multiqubit systems. Compared to low power selective pulses, which cannot average out all unwanted evolution, these pulses are substantially shorter in time, thereby reducing the effects of relaxation. Liquid-state nuclear magnetic resonance techniques on homonuclear spin systems are used to demonstrate the accuracy of these gates both in simulation and experiment. Simulations of the coherent evolution of a three-qubit system show that the control sequences faithfully implement the unitary operations, typically yielding gate fidelities on the order of 0.999 and, for some sequences, up to 0.9997. The experimentally determined density matrices resulting from the application of different control sequences on a three-spin system have overlaps of up to 0.99 with the expected states, confirming the quality of the experimental implementation.
NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.
Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch–Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch–Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch–Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.
Theoretical Quantum Information Processing (QIP) has matured from the use of qubits to the use of qudits (systems having states >2). Whereas most of the experimental implementations have been performed using qubits, little experimental work has been carried out using qudits as yet. In this paper we demonstrate experimental realization of a qutrit system by nuclear magnetic resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in liquid crystalline phase. Preparation of pseudopure states and implementation of unitary operations are demonstrated in this single-qutrit system, using transition selective pulses.