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Journal of the Graduate School of the Chinese Academy of Sciences

Quantum information processing(QIP) and realization using nuclear magnetic resonance

Da Wei

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

This paper presents our theoretical and nuclear magnetic resonance(NMR) experimental work on several QIPs including quantum super dense coding(QSDC),quantum algorithms,quantum error correction,and decoherence-free subspace.The main contents are,(1) Using NMR technique,we realize two kinds of QSDC.The experimental results show that QSDC only needs to transfer(N-1) qubits during transmitting N bits classical information;(2) On NMR quantum computers,we realize three kinds of quantum algorithms that include four-qubit summing algorithm,four-qubit Deutsch-like algorithm and seven-qubit Deutsch-Jozsa algorithm;(3) We present a quantum error correction scheme based on quantum cloning.This scheme shows the relationship between quantum cloning and quantum error correction;(4) To avoid decoherence in quantum algorithms,we construct a decoherence-free subspace(DFS) by using multiple quantum coherences.The validity of this DFS is also experimentally verified on our NMR quantum computers.The DFS makes the three unaddressed protons in a CH_3 group distinguished in two-dimensional(2D) NMR.It can protect against more error operators.This idea may provide new insights into extending the number of qubits in the sense that it effectively utilizes the magnetically equivalent nuclei.

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This paper presents our theoretical and nuclear magnetic resonance(NMR) experimental work on several QIPs including quantum super dense coding(QSDC),quantum algorithms,quantum error correction,and decoherence-free subspace.The main contents are,(1) Using NMR technique,we realize two kinds of QSDC.The experimental results show that QSDC only needs to transfer(N-1) qubits during transmitting N bits classical information;(2) On NMR quantum computers,we realize three kinds of quantum algorithms that include four-qubit summing algorithm,four-qubit Deutsch-like algorithm and seven-qubit Deutsch-Jozsa algorithm;(3) We present a quantum error correction scheme based on quantum cloning.This scheme shows the relationship between quantum cloning and quantum error correction;(4) To avoid decoherence in quantum algorithms,we construct a decoherence-free subspace(DFS) by using multiple quantum coherences.The validity of this DFS is also experimentally verified on our NMR quantum computers.The DFS makes the three unaddressed protons in a CH_3 group distinguished in two-dimensional(2D) NMR.It can protect against more error operators.This idea may provide new insights into extending the number of qubits in the sense that it effectively utilizes the magnetically equivalent nuclei.
In this study, we report an experiment realization of quantum superdense coding (QSDC) between three parties using nuclear magnetic resonance (NMR). The experimental results have shown that in terms of the QSDC schemes between multiparties proposed by Liu et al. and Crudka et al., three-qubit QSDC can transmit three bits of classical information by sending two qubits only. Our results experimentally show that quantum superdense coding, as one of the quantum information processing protocols, is superior to classical ones.
The development of quantum error correcting techniques is of paramount importance to the ultimate goal of implementing practical quantum computers. The simultaneous transmission of quantum and classical information over a quantum channel was initially investigated by Shor and since been continued by others. It was shown that there is an advantage to transmitting both quantum and classical information simultaneously, compared to independent transmissions. The characterization and construction of codes that allow to transmit both quantum and classical information, which we refer to as hybrid codes, was done from a coding theory perspective and by using the operator algebra quantum error correction (OAQEC) perspective. In this work we unify these two perspectives, showing that the coding theory formulation is a specific case of the OAQEC perspective. As a result we generalized the quantum hamming bound to the hybrid case. To date no such hybrid codes have been physically implemented. Nuclear magnetic resonance (NMR) quantum information processors (QIP) have been an excellent test bed for quantum computing. The techniques of NMR had been refined for many years and can now be applied to quantum computing. NMR techniques provides a high degree of qubit control and long decoherence times compared to other QIP. These two properties of NMR QIP make it a prime candidate for implementing hybrid codes. In this work we developed a hybrid code and designed the circuit for encoding it. We used Matlab to simulate the pulse sequence which would be used in an NMR QIP to carry out the encoding of the hybrid circuit. According to those simulations the full encoding, a single qubit Pauli error and a full decoding can be carried out without the effects of decoherence destroying the quantum information beyond retrieval.
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.
We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes a complete algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
Recent years, remarkable progresses in experimental realization of quantum information have been made, especially based on nuclear magnetic resonance (NMR) theory. In all quantum algorithms, Deutsch-Jozsa algorithm has been widely studied. It can be realized on NMR quantum computer and also can be simplified by using the Cirac's scheme. In this paper, at first the principle of Deutsch-Jozsa quantum algorithm is analyzed, then we implement the seven-qubit Deutsch-Jozsa algorithm on NMR quantum computer.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.