In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.
In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.
Pulse-based Electron–Nuclear and ELectron–electron DOuble Resonance (ENDOR/ELDOR) techniques have been applied to molecular spins in order to implement ensemble electron spin-qubit based quantum computers/computing (QC) and quantum information processing (QIP) in the solid state. Pulsed ENDOR-based QC/QIP experiments for super dense coding (SDC) have for the first time been carried out by the use of molecular electron- and nuclear-spin entities such as the stable malonyl radical as matter spin-qubits. The spin-qubit manipulation technology for quantum gate operations in this work is based on the time-proportional-phase-increment (TPPI) technique, enabling us to distinguish between the phases of spin-qubit based entangled states. The TPPI technique, as firstly applied by Mehring et al. (M. Mehring, J. Mende and W. Scherer, Phys. Rev. Lett., 2003, 90, 153001), has illustrated the establishment of quantum entanglement between electron- and nuclear-spin states and mutual interconversion between the electron–nuclear Bell states. The electron-spin 4π-periodicity in phase shows up in the QC/QIP experiments, explicitly and experimentally illustrating the electron-spin spinor nature for the first time. Tripartite QC experiments have been made, showing the occurrence of separable states. Also, the development of novel electron-spin technology to manipulate multi-electron spin-qubits is described. In this work, the pulsed coherent-dual ELDOR for QC/QIP has for the first time been implemented by invoking a novel microwave dual phase-rotation technique. Thus, applications of the coherent-dual ELDOR to molecular electron spin-qubit systems are also discussed, emphasising designing the molecular two electron-qubit systems appropriate for QC/QIP. g- and/or hyperfine A-tensor engineering approaches give us the two- and multi-electron-qubit systems, which have been a materials challenge to implement matter spin-qubit based QC/QIP. The targeted matter spin-qubits can be used to facilitate selective resonant microwave excitations achieved by the pulsed ELDOR technique. In addition to DiVincenzo's five criteria, general requisites for scalable electron spin-qubit systems as 1D periodic robust spin structures are described. According to the requisites, double- or triple-stranded helicates embedding open-shell metal cations are proposed instead of organic molecular spin-qubits.
The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.
Quantum computers are machines that exploit the quantum mechanical properties of physical systems to realize an exponential speed-up in problem-solving capability compared with existing computers. Existing schemes for the realization of such machines occur in diverse areas such as atomic physics, nuclear magnetic resonance, superconductivity, quantum optics and solid state physics. We are concerned here with the experimental realization of various elements needed for quantum information processing using nuclear spin immersed in a confined electronic system in the quantum Hall regime. Some distinguishing characteristics of this approach include the application of the Overhauser effect for dynamic nuclear polarization at relatively high temperatures, spin measurement using relatively simple electrical detection techniques, spin control with microwave/radio frequency methods, the utilization of the electronic spin exciton as a possible mobile spin transfer mechanism for the eventual realization of a logic gate, and the application of semiconductor technology to device integration. Concepts involved in this approach are also illustrated with experimental results.
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were used as qubits to implement the three-qubit Deutsch-Josza algorithm using high-resolution NMR. A classification of the Deutsch-Josza functions according to the operator representation of the corresponding oracle transformations was given. Different classes of functions may produce full, partial or no entanglement in the output states of the algorithm. This entanglement content is not immediately evident from the output states themselves. A procedure was given for mapping of the output states onto Bell- or GHZ-states by means of local transformations which preserve the entanglement content. A method for the visualization of single-spin unitary transformations was also presented. This visual representation can facilitate analysis and design of shaped rf pulses. For the purpose of quantum computing, it can be useful to suppress couplings between qubits during the application of finite-length single-qubit gates. The feasibility of this idea was demonstrated using small molecules in a liquid crystal matrix. In a series of proof-of-principle experiments, it was shown that the magic-echo sequence can be used to suppress the dipole-dipole coupling between spins and simultaneously selectively address a single spin by a soft rf pulse. The S-bus concept for spin-quantum computing holds some scalability promise and provides a testbed for studies of large, strongly coupled quantum registers. Single-crystal CaF2 weakly doped with Ce was used to implement the concept. The nine 19F nuclear spins adjacent to the paramagnetic Ce-ion serve as qubits while the electron spin plays the role of a quantum bus. The S-bus theory was tested experimentally. Procedures were given for the measurement of parameters characterizing the quantum state of the nuclear spins. An exact numeric treatment of this ten-spin system was done to aid in understanding the experimental findings. For a pair of nuclear spins with negligible direct dipolar coupling, the CNOT operation was implemented. The spin-spin coupling mediated by the bus spin was utilized for that purpose. The four Bell-states of these two distant spins were created. An experiment was performed who's signature allows those four entangled states to be distinguished. The paramagnetic cluster in CaF2:Ce is embedded in an extended network of 19F nuclear spins. This network is a powerful source of decoherence. A number of existing and a newly designed pulse sequence were tested with respect to their ability to suppress decoherence and their aptitude for use in quantum computing.
We established important relationships between entanglement measures and the order parameter (spin polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems.
Quantum computers can potentially solve real and relevant mathematical and physical problems that are intractable using classical machines. However, the experimental realization of quantum computers represents a significant challenge, because several opposing experimental requirements must be met. A set of coupled quantum bits must be manipulated and measured while coherently retaining entangled quantum states. Yet the manipulation and measurement processes almost inevitably lead to the decay of these fragile states.
This thesis work takes significant steps towards building a practical quantum computer using nuclear spins and liquid state nuclear magnetic resonance (NMR) techniques. I present experimental results for proof of principle of quantum computing in a series of small implementations of quantum algorithms, culminating in the implementation of an adiabatic quantum optimization algorithm. The performance of adiabatic algorithms compared with classical optimization methods is unknown, but small quantum computers could provide crucial insight into answering this question. Furthermore, adiabatic algorithms also shed new light on the usefulness of quantum resources for computational tasks and hence they represent an important class of algorithms.
The second part of this thesis presents several methods developed for improving the control over NMR quantum computing experiments. Even though liquid state NMR quantum computers have well known and accepted scaling limitations, the developed tools are of general use. I will show how several tools are directly transferable to two other implementations of quantum computers; one using optical methods and the other using loops of superconducting material.
This work provides insight into what is needed to build a practical quantum computer, and delivers several tools and techniques that will be useful in future large-scale implementations of quantum computers.