子空间量子计算的核磁共振实验研究
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摘要
本文的内容是关于核磁共振量子计算。量子计算是量子力学和计算机信息科学之间的新兴交叉学科,近20年来得到了快速的发展。与传统的计算机相比,基于量子力学理论的量子计算机呈现出新的特性及随之而来的优势。
随着计算机处理器的微型化趋势,芯片中的逻辑门尺寸正在接近原子尺寸,空间尺度越小,量子效应越明显。目前的理论和实验都已经显示,量子效应能被控制利用并带来通讯和计算的新模式,在某些情况下比经典情形更具有优势,信息通过物理的方法储存、传输和处理,因此,信息的产生、处理和提取实际上是一个物理的过程,信息的研究应该和相关过程的物理规律相联系。信息作为物理中一个基本概念的重要意义正在被发掘,量子信息和计算的理论把这种探索置于坚实的基础之上,并引出一些关于自然世界深刻的思考,推动产生出令人激动的自然新图景。量子密码术,量子隐形传态,量子纠错,量子计算等应用的共同点是都把量子态的叠加和纠缠等量子特性作为信息处理的基础.
量子算法的出现说明了建造量子计算机的实际意义,与经典计算机相比,处理量子信息的量子计算机能更有效地计算一些有重要意义的特殊问题。日前研究者们已经使用线性离子阱,光学系统,液体核磁共振等方法建造了少量子位数的演示性量子计算机.由于要操作和控制的量子体系在实验环境中的脆弱性,使得建造更多量子位的量子计算机非常困难。从现有的实验情况看,液体核磁共振(Nuclear MagnetiC Resonance,NMR)技术是目前最成功的量子信息处理手段之一,它为量子信息的研究提供了一个有效的测试平台。该领域研究过程中积累的丰富量子相干控制技术和研究成果,不仅为下一代的量子信息处理平台的发展提供可借鉴的经验,同时也增进了人们对量子信息科学的理解。
在丰富的量子信息研究内容中,有一类研究如何利用大的量子系统中包含的维数较低的子空间进行量子信息处理的问题。这类嵌入式的子空间量子信息处理方式对研究核磁共振Berry相位、容错避错量子计算、无噪声量子信息存储以及简化量子过程重构等课题都是很有意义的。本文的工作主要围绕子空间量子计算相关内容开展,包括以下具体内容:
利用液体核磁共振实现子空间量子计算。在实验中以C13标记丙氨酸的三个碳核自旋作为量子位,制备出α碳自旋标记的羧基碳、甲基碳两量子位子空间等效纯态,随后在该子空间里实现了Deutsch-Jozsa量子算法.实验中使用量子态重构方法重构了所制备的两量子位子空间等效纯态所在的整个体系的密度矩阵,并测量了量子态保真度,结果表明实验成功制备出子空间等效纯态。子空间内进行的Deutsch-Jozsa算法实验的结果也与理论预期很好地吻合,说明该子空间算法实验执行成功。
使用强调制脉冲方法制备子空间等效纯态。使用计算机数值搜索方法优化参数获得强调制脉冲,使量子门操作在保持选择性的情况下操作时间明显减少,因此减少了在环境干扰下系统的弛豫和量子退相干对量子门的影响。实验同时制备出2个两量子位子空间有效纯态,由实验重构出的核自旋量子系统状态与理论预期吻合。强调制脉冲门操作脉冲不仅削弱了自旋系统在内部哈密顿量作用下的明显演化,而且避免施加多个低功率脉冲在不同核自旋时引起的偏共振,实验结束时不需额外的校正。当核磁共振量子位数目增加时,系统同核自旋数目和门操作脉冲数目会随之增加,强调制脉冲能有效地保证量子门执行准确度.
在核自旋量子系统中实现两量子位子空间量子过程测量重构。量子过程重构由演化过程的—系列特定初、末态表征开放量子系统的未知动力学过程.通过它可给出量子门保真度,以便于实际量子计算中进行误差分析和相应操控.同无辅助位方法相比,具有标记位的子空间量子过程重构以付出适当的辅助量子位资源为代价,显著地缩减了试验输入的次数.对量子过程的快速准确的跟踪测量有助于及时了解量子调控的执行情况,这具有重要意义。实验中使用溶于重水的C13标记丙氨酸样品,以三个C13核自旋作为三个量子位,其中一个作为辅助位来标记另外两个量子位组成的子系统的量子态演化.考虑所用样品体系中羧基碳和甲基碳的核自旋J偶合强度很弱,在标记量子位和输入量子态选择合理,避免实验脉冲序列中使用最弱的J偶合演化等要求下,设计出初始输入态集合及相应脉冲序列操作的完整实验方案。实验执行结果与理论计算符合,完成对两量子位子空间内CNOT量子门的测量重构.
对固体自旋填充富勒烯量子计算进行探讨。量子计算机的研究发展对特定计算问题具有重要的意义,由于可控性和扩展性优势便于大规模应用的固体量子计算方案受到研究者越来越多的关注。在目前已有固体方案中,有一类基于自旋填充的富勒烯量子计算方案引起研究者比较多的兴趣。在已提出的填充富勒烯的自旋方案里,单原子N,P填充富勒烯被作为量子载体。这一方案具有很多优点,但同时也存在一些困难。譬如合成有效复合物产率很低,并且识别单个原子填充富勒烯实验困难,样品不易提纯.使用单个填充富勒烯的量子位信号很弱,不便于控制、操作和读取。对产率问题,我们提出考虑使用某些特定基团填充富勒烯团簇作为备选量子位,从而可以在一定程度上解决量子位载体样品制备困难。从单自旋信号微弱问题出发,提出一种基于填充富勒烯简单长方纳米结构的自旋系综量子位系统并考虑其在量子计算中的可能应用。
This thesis is devoted to Quantum Computation via Nuclear Magnetic Resonance. The subject of quantum computation brings together ideas from classical information theory, computer science, and quantum physics. Quantum computation is an interdisciplinary physics subject which grows very rapidly in the last two decades. Compared to traditional computer, Quantum Computer based on quantum theory has shown its new property and superiority.
With the trend of the microforming of the microprocessors, the size of the logic gates in chips is approaching atomic scale. Within atomic scale, the quantum effects will become important. Until now, theoretical and experimental results have shown that, the quantum effects may be harnessed to provide qualitatively new modes of communication and computation, in some cases much more powerful than their classical counterparts. Information is stored、transmitted and processed by physical means. Therefore, the generation, processing and retrieving of information is in fact a physical process. The research of information is related to the laws of physics closely. The full significance of information as a basic concept in physics is now being discovered. The theory of quantum information and computation puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are quantum cryptography, quantum teleportation, quantum error correction and quantum computation, etc. The common theme of all these insights is the use of quantum superposition and entanglement as a computational resource.
The appearance of quantum algorithms proves that it is essential to construct a Quantum Computer, which is fundamentally different from any computer which can only manipulate classical information. Quantum computer can solve some special problems with high efficiency, which implies that some important computational tasks are impossible to complete using any device except Quantum Computer. Currently, experimental realizations of quantum computers include linear ion trap, high-Q optical cavities, and liquid-state nuclear magnetic resonance methods.
Due to the coherent manipulation and control of the fragile quantum system in the actual experiments, it has been proved extremely difficult to practically build quantum computers. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is arguably the most successful test bed. Now, the achievements on liquid-state NMR Quantum Information Processing(QIP), especially the rich source of quantum control techniques accumulated for QIP, will contribute to the next generation of quantum information processors and the understanding of the power of QIP.
Among the various quantum information researches, there is a type of research issue, of which the characteritic is utilizing the subspace included in the bigger quantum system to handle quantum information. The embedding computation of subsystem is helpful for us to study Berry phase, error tolerant quantum computation, noiseless subspace and quantum process tomography, etc. The research content of this article focuses on the topic of subspace quantum information processing, including following related specific points:
Experimentally realizing of quantum computation in the subspace with Liquid-state Nuclear Magnetic Resonance. The three carbon nuclear spins of C13-labeled alanine CH3CH(NH2)COOH dissolved in deuterated water were used as qubits. With Liquid NMR we have realized the quantum computation in the subspace in this system. Firstly, we prepared an effective pure state in a two qubit subsystem consisting of carboxyl-carbon and methyl-carbon which is labeled byαcarbon. Secondly, The Deutsch-Jozsa quantum algorithm was also implemented in this subspace. We used quantum state tomography to reconstruct the density matrix of the effective pure state in the two qubit subspace and measured the fidelity. The result shows that the effective pure state in subspace was successfully prepared. And the spectrum corresponding to the experimental implementation of Deutsch-Jozsa algorithm in the subspace matches the theoretical predictions very well. This proves our experiments were implemented successfully.
Experimentally preparing an effective pure state in a subsystem of a three spin NMR system via an alternative method. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on 3-qubit systems. Compared with low power nuclear selective pulses scheme, Strongly Modulating Pulses scheme reduces both the number of shaped pulses and every pulse's duration obviously. In the experiment, a pair of 2-qubit subspace effective pure states in a three spin system were acquired simultaneously. The tomography for spin system is consistent with theoretical predictions, which proves that the experiment has been successfully implemented. Application of strong modulating pulses enables the pulse scheme to keep selectivity and reduce the duration of control pulses by almost an order of magnitude, therefore, significantly lessening the effects of relaxation and quantum decoherence subjected to environment noise. On the other hand, this pulse scheme avoids obvious evolution of spin-system under the action of the internal Hamiltonian. It also avoids different spins interfering with each other when they are subjected to low power pulses simultaneously. Therefore no additional corrections are required after experiments. Strong modulating pulses can be placed back to back in longer sequences, which will be increasingly useful in the future NMR QIP experiments requiring larger numbers of qubits.
Experimental investigation of two-qubit gate in subspace is implemented via the method of NMR. An unknown dynamical evolution of an open quantum system is characterized by measuring a series of initial and end state, which produces the fidelity of quantum gate, for the sake of studying the error model in practical quantum computation. At the cost of ancilla qubit resource, the number of the experiments for measuring a quantum operation can be effectively reduced. Accurate and rapid process tomogrphy enables us to acquire the timely knowledge of the actual quantum operation. The experimental sample is alanine CH3CH(NH2)COOH dissolved in deuterated water. The three nuclei labeled as C-13 are used as qubits. One of which is chosen as ancilla qubit to label the other two qubit subsystem. The experimental tomography for CNOT gate in two-qubit subspace agrees with theoretical predictions. Considering the fact that the J constant between carboxyl-carbon and methyl-carbon is very small in the alanine sample, the initial input states and corresponding pulse sequences are devised accordingly. Such as, choice of ancilla-qubit and utilization of SWAP gate to avoid applying the weakest J coupling.
A Carbon nano-anay scheme for implementing quantum computation is presented. It proposes an elementary unit and demonstrates its merits for spin qubit realization, addressing, manipulation and reading out. Firstly, Suitable isotop Trimetallic nitride Clusterfullerenes in a Carbon nano-tube array are used as qubits which have higher yeilds and high purity. Secondly, The Chain ensemble qubit contains numerous spins which can give stronger signal than a sigle molecule. Larger-sized architectures can be easily set in Si28 surface and manipulated conveniently. This kind of units can be possibly formed into large arrays to be as a architecture of scalable quantum computer.
随着计算机处理器的微型化趋势,芯片中的逻辑门尺寸正在接近原子尺寸,空间尺度越小,量子效应越明显。目前的理论和实验都已经显示,量子效应能被控制利用并带来通讯和计算的新模式,在某些情况下比经典情形更具有优势,信息通过物理的方法储存、传输和处理,因此,信息的产生、处理和提取实际上是一个物理的过程,信息的研究应该和相关过程的物理规律相联系。信息作为物理中一个基本概念的重要意义正在被发掘,量子信息和计算的理论把这种探索置于坚实的基础之上,并引出一些关于自然世界深刻的思考,推动产生出令人激动的自然新图景。量子密码术,量子隐形传态,量子纠错,量子计算等应用的共同点是都把量子态的叠加和纠缠等量子特性作为信息处理的基础.
量子算法的出现说明了建造量子计算机的实际意义,与经典计算机相比,处理量子信息的量子计算机能更有效地计算一些有重要意义的特殊问题。日前研究者们已经使用线性离子阱,光学系统,液体核磁共振等方法建造了少量子位数的演示性量子计算机.由于要操作和控制的量子体系在实验环境中的脆弱性,使得建造更多量子位的量子计算机非常困难。从现有的实验情况看,液体核磁共振(Nuclear MagnetiC Resonance,NMR)技术是目前最成功的量子信息处理手段之一,它为量子信息的研究提供了一个有效的测试平台。该领域研究过程中积累的丰富量子相干控制技术和研究成果,不仅为下一代的量子信息处理平台的发展提供可借鉴的经验,同时也增进了人们对量子信息科学的理解。
在丰富的量子信息研究内容中,有一类研究如何利用大的量子系统中包含的维数较低的子空间进行量子信息处理的问题。这类嵌入式的子空间量子信息处理方式对研究核磁共振Berry相位、容错避错量子计算、无噪声量子信息存储以及简化量子过程重构等课题都是很有意义的。本文的工作主要围绕子空间量子计算相关内容开展,包括以下具体内容:
利用液体核磁共振实现子空间量子计算。在实验中以C13标记丙氨酸的三个碳核自旋作为量子位,制备出α碳自旋标记的羧基碳、甲基碳两量子位子空间等效纯态,随后在该子空间里实现了Deutsch-Jozsa量子算法.实验中使用量子态重构方法重构了所制备的两量子位子空间等效纯态所在的整个体系的密度矩阵,并测量了量子态保真度,结果表明实验成功制备出子空间等效纯态。子空间内进行的Deutsch-Jozsa算法实验的结果也与理论预期很好地吻合,说明该子空间算法实验执行成功。
使用强调制脉冲方法制备子空间等效纯态。使用计算机数值搜索方法优化参数获得强调制脉冲,使量子门操作在保持选择性的情况下操作时间明显减少,因此减少了在环境干扰下系统的弛豫和量子退相干对量子门的影响。实验同时制备出2个两量子位子空间有效纯态,由实验重构出的核自旋量子系统状态与理论预期吻合。强调制脉冲门操作脉冲不仅削弱了自旋系统在内部哈密顿量作用下的明显演化,而且避免施加多个低功率脉冲在不同核自旋时引起的偏共振,实验结束时不需额外的校正。当核磁共振量子位数目增加时,系统同核自旋数目和门操作脉冲数目会随之增加,强调制脉冲能有效地保证量子门执行准确度.
在核自旋量子系统中实现两量子位子空间量子过程测量重构。量子过程重构由演化过程的—系列特定初、末态表征开放量子系统的未知动力学过程.通过它可给出量子门保真度,以便于实际量子计算中进行误差分析和相应操控.同无辅助位方法相比,具有标记位的子空间量子过程重构以付出适当的辅助量子位资源为代价,显著地缩减了试验输入的次数.对量子过程的快速准确的跟踪测量有助于及时了解量子调控的执行情况,这具有重要意义。实验中使用溶于重水的C13标记丙氨酸样品,以三个C13核自旋作为三个量子位,其中一个作为辅助位来标记另外两个量子位组成的子系统的量子态演化.考虑所用样品体系中羧基碳和甲基碳的核自旋J偶合强度很弱,在标记量子位和输入量子态选择合理,避免实验脉冲序列中使用最弱的J偶合演化等要求下,设计出初始输入态集合及相应脉冲序列操作的完整实验方案。实验执行结果与理论计算符合,完成对两量子位子空间内CNOT量子门的测量重构.
对固体自旋填充富勒烯量子计算进行探讨。量子计算机的研究发展对特定计算问题具有重要的意义,由于可控性和扩展性优势便于大规模应用的固体量子计算方案受到研究者越来越多的关注。在目前已有固体方案中,有一类基于自旋填充的富勒烯量子计算方案引起研究者比较多的兴趣。在已提出的填充富勒烯的自旋方案里,单原子N,P填充富勒烯被作为量子载体。这一方案具有很多优点,但同时也存在一些困难。譬如合成有效复合物产率很低,并且识别单个原子填充富勒烯实验困难,样品不易提纯.使用单个填充富勒烯的量子位信号很弱,不便于控制、操作和读取。对产率问题,我们提出考虑使用某些特定基团填充富勒烯团簇作为备选量子位,从而可以在一定程度上解决量子位载体样品制备困难。从单自旋信号微弱问题出发,提出一种基于填充富勒烯简单长方纳米结构的自旋系综量子位系统并考虑其在量子计算中的可能应用。
This thesis is devoted to Quantum Computation via Nuclear Magnetic Resonance. The subject of quantum computation brings together ideas from classical information theory, computer science, and quantum physics. Quantum computation is an interdisciplinary physics subject which grows very rapidly in the last two decades. Compared to traditional computer, Quantum Computer based on quantum theory has shown its new property and superiority.
With the trend of the microforming of the microprocessors, the size of the logic gates in chips is approaching atomic scale. Within atomic scale, the quantum effects will become important. Until now, theoretical and experimental results have shown that, the quantum effects may be harnessed to provide qualitatively new modes of communication and computation, in some cases much more powerful than their classical counterparts. Information is stored、transmitted and processed by physical means. Therefore, the generation, processing and retrieving of information is in fact a physical process. The research of information is related to the laws of physics closely. The full significance of information as a basic concept in physics is now being discovered. The theory of quantum information and computation puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are quantum cryptography, quantum teleportation, quantum error correction and quantum computation, etc. The common theme of all these insights is the use of quantum superposition and entanglement as a computational resource.
The appearance of quantum algorithms proves that it is essential to construct a Quantum Computer, which is fundamentally different from any computer which can only manipulate classical information. Quantum computer can solve some special problems with high efficiency, which implies that some important computational tasks are impossible to complete using any device except Quantum Computer. Currently, experimental realizations of quantum computers include linear ion trap, high-Q optical cavities, and liquid-state nuclear magnetic resonance methods.
Due to the coherent manipulation and control of the fragile quantum system in the actual experiments, it has been proved extremely difficult to practically build quantum computers. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is arguably the most successful test bed. Now, the achievements on liquid-state NMR Quantum Information Processing(QIP), especially the rich source of quantum control techniques accumulated for QIP, will contribute to the next generation of quantum information processors and the understanding of the power of QIP.
Among the various quantum information researches, there is a type of research issue, of which the characteritic is utilizing the subspace included in the bigger quantum system to handle quantum information. The embedding computation of subsystem is helpful for us to study Berry phase, error tolerant quantum computation, noiseless subspace and quantum process tomography, etc. The research content of this article focuses on the topic of subspace quantum information processing, including following related specific points:
Experimentally realizing of quantum computation in the subspace with Liquid-state Nuclear Magnetic Resonance. The three carbon nuclear spins of C13-labeled alanine CH3CH(NH2)COOH dissolved in deuterated water were used as qubits. With Liquid NMR we have realized the quantum computation in the subspace in this system. Firstly, we prepared an effective pure state in a two qubit subsystem consisting of carboxyl-carbon and methyl-carbon which is labeled byαcarbon. Secondly, The Deutsch-Jozsa quantum algorithm was also implemented in this subspace. We used quantum state tomography to reconstruct the density matrix of the effective pure state in the two qubit subspace and measured the fidelity. The result shows that the effective pure state in subspace was successfully prepared. And the spectrum corresponding to the experimental implementation of Deutsch-Jozsa algorithm in the subspace matches the theoretical predictions very well. This proves our experiments were implemented successfully.
Experimentally preparing an effective pure state in a subsystem of a three spin NMR system via an alternative method. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on 3-qubit systems. Compared with low power nuclear selective pulses scheme, Strongly Modulating Pulses scheme reduces both the number of shaped pulses and every pulse's duration obviously. In the experiment, a pair of 2-qubit subspace effective pure states in a three spin system were acquired simultaneously. The tomography for spin system is consistent with theoretical predictions, which proves that the experiment has been successfully implemented. Application of strong modulating pulses enables the pulse scheme to keep selectivity and reduce the duration of control pulses by almost an order of magnitude, therefore, significantly lessening the effects of relaxation and quantum decoherence subjected to environment noise. On the other hand, this pulse scheme avoids obvious evolution of spin-system under the action of the internal Hamiltonian. It also avoids different spins interfering with each other when they are subjected to low power pulses simultaneously. Therefore no additional corrections are required after experiments. Strong modulating pulses can be placed back to back in longer sequences, which will be increasingly useful in the future NMR QIP experiments requiring larger numbers of qubits.
Experimental investigation of two-qubit gate in subspace is implemented via the method of NMR. An unknown dynamical evolution of an open quantum system is characterized by measuring a series of initial and end state, which produces the fidelity of quantum gate, for the sake of studying the error model in practical quantum computation. At the cost of ancilla qubit resource, the number of the experiments for measuring a quantum operation can be effectively reduced. Accurate and rapid process tomogrphy enables us to acquire the timely knowledge of the actual quantum operation. The experimental sample is alanine CH3CH(NH2)COOH dissolved in deuterated water. The three nuclei labeled as C-13 are used as qubits. One of which is chosen as ancilla qubit to label the other two qubit subsystem. The experimental tomography for CNOT gate in two-qubit subspace agrees with theoretical predictions. Considering the fact that the J constant between carboxyl-carbon and methyl-carbon is very small in the alanine sample, the initial input states and corresponding pulse sequences are devised accordingly. Such as, choice of ancilla-qubit and utilization of SWAP gate to avoid applying the weakest J coupling.
A Carbon nano-anay scheme for implementing quantum computation is presented. It proposes an elementary unit and demonstrates its merits for spin qubit realization, addressing, manipulation and reading out. Firstly, Suitable isotop Trimetallic nitride Clusterfullerenes in a Carbon nano-tube array are used as qubits which have higher yeilds and high purity. Secondly, The Chain ensemble qubit contains numerous spins which can give stronger signal than a sigle molecule. Larger-sized architectures can be easily set in Si28 surface and manipulated conveniently. This kind of units can be possibly formed into large arrays to be as a architecture of scalable quantum computer.
引文
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