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arXiv:0704.1181

Simulation of four-body interaction in a nuclear magnetic resonance quantum information processor

Wen-Zhang Liu, Jinfu Zhang, Long, Gui Lu

Published Apr 10, 2007• 0 citations
arXivHTMLPDF

Abstract

Four-body interaction plays an important role in many-body systems, and it can exhibit interesting phase transition behaviors. Historically it was the need to efficiently simulate quantum systems that lead the idea of a quantum computer. In this Letter, we report the experimental demonstration of a four-body interaction in a four- qubit nuclear magnetic resonance quantum information processor. The strongly modulating pulse is used to implement spin selective excitation. The results show a good agreement between theory and experiment.

DOI
10.48550/arxiv.0704.1181

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Four-body interaction plays an important role in many-body systems, and it can exhibit interesting phase transition behaviors. Historically it was the need to efficiently simulate quantum systems that lead the idea of a quantum computer. In this Letter, we report the experimental demonstration of a four-body interaction in a four- qubit nuclear magnetic resonance quantum information processor. The strongly modulating pulse is used to implement spin selective excitation. The results show a good agreement between theory and experiment.
We demonstrate the implementation of an entanglement swapping operation on a four-qubit liquid-state nuclear-magnetic-resonance (NMR) quantum-information processor. We use this experiment as a benchmark to illustrate the progress made in the field of quantum control using strongly modulating pulses and a correction scheme for removing distortions introduced by the nonlinearities in the transmitter and probe circuits. The advances include compensating for incoherent errors caused by the spatial variation of the system Hamiltonian in the NMR sample. The goal of these control sequences is to cause the collapse of the Kraus operator-sum representation of the superoperator into one unitary operator so that the ensemble appears to evolve as one coherent whole.
NMR quantum computing with qubit systems represented by nuclear spins (I=12) in small molecules in liquids has led to the most successful experimental quantum information processors so far. We use the quadrupolar spin-32 sodium nuclei of a NaNO3 single crystal as a virtual two-qubit system. The large quadrupolar coupling in comparison with the environmental interactions and the usage of strongly modulating pulses allow us to manipulate the system fast enough and at the same time keeping the decoherence reasonably slow. The experimental challenge is to characterize the "calculation" behavior of the quantum processor by process tomography which is here adapted to the quadrupolar spin system. The results of a selection of quantum gates and algorithms are presented as well as a detailed analysis of experimental results.
Optimal labeling schemes lead to efficient experimental protocols for quantum-information processing by nuclear magnetic resonance (NMR). A systematic approach to finding optimal labeling schemes for a given computation is described here. The scheme is described for both quadrupolar systems and spin-12\frac{1}{2}21​ systems. Using the technique of transition selective pulses, one of the optimal labeling schemes has been applied to experimentally implement a quantum full adder in a four-qubit system by NMR.
With the development of quantum information and quantum computation science, quantum information processor has been widely used in different areas such as quantum simulation, quantum computation and quantum metrology and so on. To make quantum computer come true, we need to increase the number of controllable qubits of the system and improve the controllability to perform complex quantum manipulation. As a good experimental testbed for quantum information processing, nuclear magnetic resonance (NMR) spin system provides rich and sophisticated quantum control methods. In recent years a lot of multi-qubit experiments have been performed on the platform and a series of experimental technologies have been developed. In this paper, we firstly explain the difficulties of multi-qubit NMR experiments. Then by focusing on the experiment of 7-qubit labelled pseudo-pure state preparation and other relevant experiments, we review the technologies in multi-qubit experiments. Using the radio frequency selective method, the inhomogeneities of the radio frequency pulses are reduced and the spectral resolution is improved. After performing 1/2 spin selective sequence, we can regard the three methyl protons in the sample of crotonic acid as a single 1/2 spin nucleus and treat the whole molecule as a 7-qubit quantum information processor. We utilize Gauss pulses, Hermite pulses, composite pulses and gradient ascent pulse engineering (GRAPE) pulses to implement basic /2 and rotation operations. The GRAPE pulses are calculated by subspace GRAPE program to speed up the computation greatly. The errors of the basic pulses caused by chemical shift and J-coupling evolution can be estimated by the program of pulse compilation. It divides the errors of the pulses into a series of post-errors and pre-errors. A program of sequence compilation is used to eliminate the accumulated error of the whole pulse sequence, reduce the number of pulses and optimize the experimental duration. A variety of methods of quantum state tomography have been proposed to improve the efficiency of reading out information about quantum state. As an experimental example, we combine the above experimental technologies and perform the experiment of 7-qubit labelled pseudo-pure state preparation by using the method of cat state preparation. The sequence of cat state preparation consists of three steps:encoding procedure, phase cycling and decoding procedure. We use 14 experiments to realize the phase cycling and acquire the final 7-qubit labelled pseudo-pure state. The total duration of experimental sequence is about 132 ms. All the readout spectra have the similar shapes to the theoretical expectations. Finally we give an outlook for further research in this direction.
We report the implementation of an entanglement transfer on a four-qubit liquid-state nuclear-magnetic resonance quantum information processor. This consists of creating an (pseudopure) entangled state among two directly coupled spins, and then transferring this two-spin state to another pair of spins whose direct interactions are negligible. Such transfers are expected to be an essential operation in scalable quantum computer architectures, and provide a useful benchmark for the coherent control available in specific implementations.