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Realization of Seven-qubit Deutsch-Jozsa Algorithm on NMR Quantum Computer

Wei Da-xiu

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

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.

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IEEE International Advance Computing Conference•Feb 1, 2014•1 citation
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.
Schemes of experimental realization of the main two-qubit processors for quantum computers and the Deutsch-Jozsa algorithm are derived in virtual spin representation. The results are applicable for every four quantum states allowing the required properties for quantum processor implementation if for qubit encoding, virtual spin representation is used. A four-dimensional Hilbert space of nuclear spin 3/23/23/2 is considered in detail for this aim.
A new approach to the implementation of a quantum computer by high-resolution nuclear magnetic resonance (NMR) is described. The key feature is that two or more line-selective radio-frequency pulses are applied simultaneously. A three-qubit quantum computer has been investigated using the 400 MHz NMR spectrum of the three coupled protons in 2,3-dibromopropanoic acid. It has been employed to implement the Deutsch-Jozsa algorithm for distinguishing between constant and balanced functions. The extension to systems containing more coupled spins is straightforward and does not require a more protracted experiment.
Quantum adiabatic algorithms is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. The adiabatic Deutsch-Jozsa algorithm given be Saurya Das, Randy Kobes and Gabor Kunstatter [Phys. Rev. A. 65, 062301 (2002)], shows how the Deutsch-Jozsa algorithm can be implemented in N^{1/2} steps, where N=2^n and n is the number of qubits, using local adiabatic evolution. In this paper we report the experimental implementation of the adiabatic Deutsch-Jozsa algorithm in a two qubit quantum information processor by Nuclear Magnetic Resonance.
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 the experimental realization of seven-qubit Deutsch-Jozsa (D-J) algorithm and controlled phase-shift gates with improved precision using liquid state nuclear magnetic resonance (NMR). The experimental results have shown that transformationsU f in the seven-qubit D-J algorithm have been implemented with different pulse sequences, and whetherf is constant or balanced is determined by using only a single function call (U f ). Furthermore, we propose an experimental method to measure and correct the error in the controlled phase-shift gate that is simple and feasible in experiments, and can have precise phase shifts. These may offer the possibility of surmounting the difficulties of low signal-to-noise ratio (SNR) in multi-qubit NMR quantum computers, more complicated experimental techniques, and the increase of gate errors due to using a large number of imperfect selective pulses. These are also applied to more complicated quantum algorithms with more qubits, such as quantum Fourier transformation and Shor’s algorithm.
Quantum Computation is slowly evolving as the next big innovation that would change the entire way we perceive the world around us. Even though many scientists are actively researching on it, one main hurdle is that a physical quantum computer is not readily available to everyone to work on. The present paper computationally simulates a quantum algorithm using nuclear magnetic resonance on four different kinds of molecules and shows that the spectra obtained are similar to the experimental results. Computational simulations like these would allow researchers to verify their quantum algorithms using NMR without actually having a physical device hence overcoming the hurdle.