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NMR experimental realization of seven-qubit DJ algorithm and controlled phase-shift gates with improved precision

Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Chinese Academy of Sciences, Peping, Beijing, China
Chinese Science Bulletin (Impact Factor: 1.37). 02/2003; 48(3):239-243. DOI: 10.1007/BF03183290

ABSTRACT 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.

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    • "Since, however, the idea of quantum computation is based on the concept of being able to manipulate the spin dynamics on the basis of pure quantum spin states, there have been various attempts at implementing quantum computation algorithms using the experimental conditions and restrictions of NMR by adopting pseudo-pure spin state based approaches. The most commonly implemented quantum algorithm, both in NMR and in general, is the one due to Deutsch and Josza [8] [23] [9] [10] [14] [20] [26] [3] [24] [19] [21] [11] [29] [25] [16] [15] [18]. The various NMR implementations differ by: the underlying spin quantum numbers S (S = 1/2 or S > 1/2); the initial spin states (thermal equilibrium state or pseudo pure state); the algorithmic implementation of the problem (Collins [8] or Cleve [7] defining the number of qubits necessary to operate a given DJ problem size). "
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