核磁共振量子计算中的实验技术
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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出。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之一。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。
在本文中,我们从核磁共振量子计算技术开始,说明了如何利用NMR体系来完成量子计算任务,并详细介绍了NMR核磁共振实验中的强调制脉冲技术。通过使用强调制脉冲和梯度场脉冲等技术,我们完成了一些实验:实验观测了混态几何相(Uhlmann相和Sjo¨qvist相),并把它们统一到同一个框架中,这是Uhlmann几何相的首次实验观测。此外,还实验观测了拓扑相,它和SO(3)的双连通性质有着直接的关系。这些相位的实验观测,能对几何相和拓扑相量子计算的发展,起到推动的作用。我们还实现了DJ算法的单向量子计算,这个是液体核磁共振体系中单向量子算法的第一次实验实现,而且是在一个与线性4量子比特图态不同的图态上实现的。通过这里运用到的系综量子计算技术,我们发现在这个实验中不需要用到主动的前反馈,实验的计算结果依然是确定和正确的。这个独特和有趣的特点避免了主动反馈实现的技术难度。最后,我们讨论了液晶体系中的量子计算实验技术,并研究了各种赝纯态的制备方法。通过我们的工作,找到了一个新的简单易行的方法来实现赝纯态的制备,并通过了实验的检验。
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,从液体和液晶中发展起来的量子态相干控制技术将来可能被用到固体量子计算中,或者其它量子体系,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 ma-chine which works grounding on quantum mechanics theory and has intense superi-ority over the classical computer on processing complicated computational problems.Quantum computer can solve some certain problems which are NP ones for their classi-cal counterparts, and Shor’s quantum algorithm for prime factorization is a well-knowninstance. As the experimental implementation of quantum computation need initial-ization,coherent manipulation,control and read of the fragile quantum system, practi-cally building quantum computers has proved extremely difficult. However, of the ex-tant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successfulone. Using mature NMR technique, preparing initial states and manipulating quantumgates are both realized. To this day the coherent control of 12 qubits has been imple-mented. Many quantum algorithms are demonstrated on the level of small numbers ofqubits. The experiments have proven the feasibility of quantum computation, whichspirits up us to study quantum computation further.
In this thesis, we started from the basic computational technologies of NMR,demonstrated that how to realize quantum computation by using NMR system. Thenwe introduced the strongly modulating pulses (SMP), and by using this technologyand gradient pulses we finished some experiments. We experimental demonstrated theunified framework for the mixed state geometric phase (Uhlmann phase andSjo¨qvistphase) and clearly demonstrated that their unification is possible. Our experiments arefurthermore the first such to measure Uhlmann’s mixed state geometric phase and showin addition that it is different to the Sjo¨qvist’s phase. We also experimental observeda topological phase in the maximally entangled state of a pair of qubits, the differentbehavior of topological phase is directly related to the double connectedness of SO(3).These results may be relevant for geometric and topological quantum computations.We also have designed and demonstrated an one-way based realization of the DJ algo-rithm on a star-like four-qubit graph state. This is the first one-way experiment reportedwhich is performed in the liquid-state NMR system and on a state other than the lin-ear four-qubit cluster state. Due to the ensemble quantum computing technology usedhere, we find no active feed-forward is needed in our experiment yet the computation is still deterministic and correct. This unique and interesting feature avoids the technicalchallenges in realizing the active feed-forward. Finally, we discussed the experimentaltechnologies used in liquid-crystal NMR syatem, and studied several methods to pre-pare the pseudo-pure state (PPS) from the thermal state of this system. In our work, wefind a easy way to prepare the PPS, also a experimental demostration was performed.
These works have given us much practical experience of what it takes to build aquantum computer. The quantum coherence controlling techniques developed for liq-uid and liquid crystal NMR may find use in solid NMR or other, perhaps more scalablequantum computer implementations.
在本文中,我们从核磁共振量子计算技术开始,说明了如何利用NMR体系来完成量子计算任务,并详细介绍了NMR核磁共振实验中的强调制脉冲技术。通过使用强调制脉冲和梯度场脉冲等技术,我们完成了一些实验:实验观测了混态几何相(Uhlmann相和Sjo¨qvist相),并把它们统一到同一个框架中,这是Uhlmann几何相的首次实验观测。此外,还实验观测了拓扑相,它和SO(3)的双连通性质有着直接的关系。这些相位的实验观测,能对几何相和拓扑相量子计算的发展,起到推动的作用。我们还实现了DJ算法的单向量子计算,这个是液体核磁共振体系中单向量子算法的第一次实验实现,而且是在一个与线性4量子比特图态不同的图态上实现的。通过这里运用到的系综量子计算技术,我们发现在这个实验中不需要用到主动的前反馈,实验的计算结果依然是确定和正确的。这个独特和有趣的特点避免了主动反馈实现的技术难度。最后,我们讨论了液晶体系中的量子计算实验技术,并研究了各种赝纯态的制备方法。通过我们的工作,找到了一个新的简单易行的方法来实现赝纯态的制备,并通过了实验的检验。
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,从液体和液晶中发展起来的量子态相干控制技术将来可能被用到固体量子计算中,或者其它量子体系,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 ma-chine which works grounding on quantum mechanics theory and has intense superi-ority over the classical computer on processing complicated computational problems.Quantum computer can solve some certain problems which are NP ones for their classi-cal counterparts, and Shor’s quantum algorithm for prime factorization is a well-knowninstance. As the experimental implementation of quantum computation need initial-ization,coherent manipulation,control and read of the fragile quantum system, practi-cally building quantum computers has proved extremely difficult. However, of the ex-tant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successfulone. Using mature NMR technique, preparing initial states and manipulating quantumgates are both realized. To this day the coherent control of 12 qubits has been imple-mented. Many quantum algorithms are demonstrated on the level of small numbers ofqubits. The experiments have proven the feasibility of quantum computation, whichspirits up us to study quantum computation further.
In this thesis, we started from the basic computational technologies of NMR,demonstrated that how to realize quantum computation by using NMR system. Thenwe introduced the strongly modulating pulses (SMP), and by using this technologyand gradient pulses we finished some experiments. We experimental demonstrated theunified framework for the mixed state geometric phase (Uhlmann phase andSjo¨qvistphase) and clearly demonstrated that their unification is possible. Our experiments arefurthermore the first such to measure Uhlmann’s mixed state geometric phase and showin addition that it is different to the Sjo¨qvist’s phase. We also experimental observeda topological phase in the maximally entangled state of a pair of qubits, the differentbehavior of topological phase is directly related to the double connectedness of SO(3).These results may be relevant for geometric and topological quantum computations.We also have designed and demonstrated an one-way based realization of the DJ algo-rithm on a star-like four-qubit graph state. This is the first one-way experiment reportedwhich is performed in the liquid-state NMR system and on a state other than the lin-ear four-qubit cluster state. Due to the ensemble quantum computing technology usedhere, we find no active feed-forward is needed in our experiment yet the computation is still deterministic and correct. This unique and interesting feature avoids the technicalchallenges in realizing the active feed-forward. Finally, we discussed the experimentaltechnologies used in liquid-crystal NMR syatem, and studied several methods to pre-pare the pseudo-pure state (PPS) from the thermal state of this system. In our work, wefind a easy way to prepare the PPS, also a experimental demostration was performed.
These works have given us much practical experience of what it takes to build aquantum computer. The quantum coherence controlling techniques developed for liq-uid and liquid crystal NMR may find use in solid NMR or other, perhaps more scalablequantum computer implementations.
引文
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