量子计算的核磁共振实验实现
摘要
量子计算研究的根本目标是建造基于量子力学原理,能在许多复杂计算问题上大大超越经典计算机性能的新型计算机。作为经典计算方式的继承,量子计算能有效处理一类计算问题,这些问题在经典计算科学中具有相当计算复杂度甚至无法完成,比如大数的质因数分解。量子计算机的实验实现需要对脆弱的量子体系进行初始化,相干控制和操作以及读。要建立一种能够满足各方面要求的量子计算机是非常困难的。相比较而言,核磁共振是当前技术上最为成熟的量子计算实验手段。利用成熟的传统磁共振技术,人们完成了初态制备、量子逻辑门操作,实现了12量子比特的相干调控(迄今最大数量的量子比特操控),大量的量子算法也已在低量子位水平上得到了验证。这些实验验证了量子计算的可行性,给予了人们研究量子计算机的极大信心。
在本论文中,我们利用NMR技术实验验证了一些重要的量子计算问题。主要工作有:实验实现了态依赖的量子态克隆,这在量子通信和量子密码领域具有重要意义:实验演示了一个非常实用的量子器件,利用它可以非常方便的测量未知量子态的信息而不需要进行量子层析;对于一些量子算法比如随机行走搜索算法我们也给予了实验验证,这个算法能达到和Grover算法相同的搜索提速;实现量子计算最关键的一点是要将噪声压制在一定的限度内,为研究抗噪声量子计算的实验实现,我们集中考虑了作为容错量子计算方案中的重要一员的几何量子计算,我们在国际上首次测量了混念几何相,并利用非传统的几何相搭建了高精度的通用量子逻辑门,以及测量了非对角几何相的性质。
固态NMR构建可扩展的量子信息处理可以被寄予厚望,我们对固态NMR量子计算实验实现上也进行了一些初步的探讨。
这些实验工作为我们最终实现量子计算积累了丰富的实际经验,从液体和固体中发展起来的量子态相干控制技术将来可能被用到其它量子体系,甚至是可扩展的量子计算机实现中。
The basic aim of research on quantum computation is to construct a new machine which works grounding on quantum mechanics theory and has intense superiority over the classical computer on processing complicated computational problems. Quantum computer can solve some certain problems which are NP ones for their classical counterparts, and Shor's quantum algorithm for prime factorization is a well-known instance. As the experimental implementation of quantum computation need initialization, coherent manipulation,control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successful one. Using mature NMR technique, preparing initial states and manipulating quantum gates are both realized. To this day the coherent control of 12 qubits has been implemented. Many quantum algorithms are demonstrated on the level of small numbers of qubits. The experiments have proven the feasibility of quantum computation, which spirits up us to study quantum computation further.
In this thesis, we concentrate on some important problems and algorithms concerning robustness against noise in quantum computation.
We demonstrate some important quantum protocols in quantum computation use NMR technique. The main research results are as follows. We report the first experimental optimal quantum state-dependent cloner. Besides, we demonstrate an important building block which perform various quantum information processing tasks directly without recourse to quantum tomography, and realize a quantum random walk search algorithm which has a speedup similar to the Grover's quantum search algorithm.
To experimental realization of quantum computation, suppressing the noises to an acceptable level is one of the most important problems. Using liquid NMR system, we have studied geometrical quantum computation which is one method to achieve built-in fault tolerant quantum gates with higher fidelities. We have first observed the geometrical phase of the mixed state, implemented high-fidelity unconventional geo- metric quantum gates, and measure the off diagonal geometric phase. Farther, some underway study on solid state system is carried out.
This work has given us much practical experience of what it takes to build a quantum computer. The quantum coherence controlling techniques developed for liquid and solid NMR may find use in other, perhaps more scalable quantum computer implementations.
在本论文中,我们利用NMR技术实验验证了一些重要的量子计算问题。主要工作有:实验实现了态依赖的量子态克隆,这在量子通信和量子密码领域具有重要意义:实验演示了一个非常实用的量子器件,利用它可以非常方便的测量未知量子态的信息而不需要进行量子层析;对于一些量子算法比如随机行走搜索算法我们也给予了实验验证,这个算法能达到和Grover算法相同的搜索提速;实现量子计算最关键的一点是要将噪声压制在一定的限度内,为研究抗噪声量子计算的实验实现,我们集中考虑了作为容错量子计算方案中的重要一员的几何量子计算,我们在国际上首次测量了混念几何相,并利用非传统的几何相搭建了高精度的通用量子逻辑门,以及测量了非对角几何相的性质。
固态NMR构建可扩展的量子信息处理可以被寄予厚望,我们对固态NMR量子计算实验实现上也进行了一些初步的探讨。
这些实验工作为我们最终实现量子计算积累了丰富的实际经验,从液体和固体中发展起来的量子态相干控制技术将来可能被用到其它量子体系,甚至是可扩展的量子计算机实现中。
The basic aim of research on quantum computation is to construct a new machine which works grounding on quantum mechanics theory and has intense superiority over the classical computer on processing complicated computational problems. Quantum computer can solve some certain problems which are NP ones for their classical counterparts, and Shor's quantum algorithm for prime factorization is a well-known instance. As the experimental implementation of quantum computation need initialization, coherent manipulation,control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successful one. Using mature NMR technique, preparing initial states and manipulating quantum gates are both realized. To this day the coherent control of 12 qubits has been implemented. Many quantum algorithms are demonstrated on the level of small numbers of qubits. The experiments have proven the feasibility of quantum computation, which spirits up us to study quantum computation further.
In this thesis, we concentrate on some important problems and algorithms concerning robustness against noise in quantum computation.
We demonstrate some important quantum protocols in quantum computation use NMR technique. The main research results are as follows. We report the first experimental optimal quantum state-dependent cloner. Besides, we demonstrate an important building block which perform various quantum information processing tasks directly without recourse to quantum tomography, and realize a quantum random walk search algorithm which has a speedup similar to the Grover's quantum search algorithm.
To experimental realization of quantum computation, suppressing the noises to an acceptable level is one of the most important problems. Using liquid NMR system, we have studied geometrical quantum computation which is one method to achieve built-in fault tolerant quantum gates with higher fidelities. We have first observed the geometrical phase of the mixed state, implemented high-fidelity unconventional geo- metric quantum gates, and measure the off diagonal geometric phase. Farther, some underway study on solid state system is carried out.
This work has given us much practical experience of what it takes to build a quantum computer. The quantum coherence controlling techniques developed for liquid and solid NMR may find use in other, perhaps more scalable quantum computer implementations.
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