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Chinese Science Bulletin (Chinese Version)

用控制非(CNOT)门组合法制备核自旋系综的有效纯态

希茄 缪, 晓冬 杨, 达秀 魏, 军 罗

Published Oct 1, 2002• 0 citations
Publisher

Abstract

核磁共振(NMR)是研究量子计算的实验方法之一, 大多数用核自旋系综实现的量子算法的初始态均为有效纯态, 因而制备出有效纯态是进行核磁共振量子计算的基础. 迄今为止, 如何制备有效纯态已提出了多种方案. 根据控制非(CNOT)门组合法的理论, 分析了奇数位和偶数位量子体系制备有效纯态的特点, 并设计了制备4量子位核自旋体系有效纯态的脉冲程序, 在实验上获得了实现. 这种方法减少了实验的复杂程度, 并具有较高的信噪比.

DOI
10.1360/csb2002-47-19-1460

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核磁共振(NMR)是研究量子计算的实验方法之一, 大多数用核自旋系综实现的量子算法的初始态均为有效纯态, 因而制备出有效纯态是进行核磁共振量子计算的基础. 迄今为止, 如何制备有效纯态已提出了多种方案. 根据控制非(CNOT)门组合法的理论, 分析了奇数位和偶数位量子体系制备有效纯态的特点, 并设计了制备4量子位核自旋体系有效纯态的脉冲程序, 在实验上获得了实现. 这种方法减少了实验的复杂程度, 并具有较高的信噪比.
核磁共振(NMR)是研究量子计算的实验方法之一, 大多数用核自旋系综实现的量子算法的初始态均为有效纯态, 因而制备出有效纯态是进行核磁共振量子计算的基础. 迄今为止, 如何制备有效纯态已提出了多种方案. 根据控制非(CNOT)门组合法的理论, 分析了奇数位和偶数位量子体系制备有效纯态的特点, 并设计了制备4量子位核自旋体系有效纯态的脉冲程序, 在实验上获得了实现. 这种方法减少了实验的复杂程度, 并具有较高的信噪比.
Abstract In nuclear magnetic resonance (NMR) quantum computing systems, it is very important to prepare an effective pure state rather than a true pure state. Our main objective is to present a general algorithm that provides quantum circuits for preparing an effective pure state from any mixed state, consisting only of controlled‐not (CNOT) quantum gates for homonuclear spin systems. Our algorithm is based on the product operator approach and could be applicable to NMR quantum computing systems with more than eight qubits. Optimization of the number of controlled‐not quantum gates is discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
CNOT门是量子计算中重要的量子元件，尤其是在量子线路中的容错扩展矩形构造中应用广泛。然而，由于CNOT门扩展矩形容错构造中的容错辅助态的制备线路一般较为复杂，给CNOT门扩展矩形容错构造的设计与实现带来了不便。基于重叠法，提出一种新的（49，1，9）量子纠错码CNOT门扩展矩形容错构造，并简化了CNOT门扩展矩形容错构造的量子线路。研究结果表明：基于重叠法的CNOT门扩展矩形容错构造中所需要的CNOT门开销比传统的拉丁矩形法制备少224个。
Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.