Experimental Investigation Of Subspace Quantum Computation Via Nuclear Magnetic Resonance

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.