Nuclear magnetic resonance (NMR) is a spectroscopic method that can be applied to several areas. Currently, this technique is also being used as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The present work is devoted to studying heavy metal complexes as possible candidates to act as qubit molecules. Nuclei such 113Cd, 199Hg, 125Te, and 77Se assembled with the most common employed nuclei in NMR-QIP implementations (1H, 13C, 19F, 29Si, and 31P) could potentially be used in heteronuclear systems for NMR-QIP implementations. Hence, aiming to contribute to the development of future scalable heteronuclear spin systems, we specially designed four complexes, based on the auspicious qubit systems proposed in our previous work, which will be explored by quantum chemical calculations of their NMR parameters and proposed as suitable qubit molecules. Chemical shifts and spin–spin coupling constants in four complexes were examined using the spin–orbit zeroth-order regular approximation (ZORA) at the density functional theory (DFT) level, as well as the relaxation parameters (T1 and T2). Examining the required spectral properties of NMR-QIP, all the designed complexes were found to be promising candidates for qubit molecules.
Nuclear magnetic resonance (NMR) is a spectroscopic method that can be applied to several areas. Currently, this technique is also being used as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The present work is devoted to studying heavy metal complexes as possible candidates to act as qubit molecules. Nuclei such 113Cd, 199Hg, 125Te, and 77Se assembled with the most common employed nuclei in NMR-QIP implementations (1H, 13C, 19F, 29Si, and 31P) could potentially be used in heteronuclear systems for NMR-QIP implementations. Hence, aiming to contribute to the development of future scalable heteronuclear spin systems, we specially designed four complexes, based on the auspicious qubit systems proposed in our previous work, which will be explored by quantum chemical calculations of their NMR parameters and proposed as suitable qubit molecules. Chemical shifts and spin–spin coupling constants in four complexes were examined using the spin–orbit zeroth-order regular approximation (ZORA) at the density functional theory (DFT) level, as well as the relaxation parameters (T1 and T2). Examining the required spectral properties of NMR-QIP, all the designed complexes were found to be promising candidates for qubit molecules.
Today the trend is to automate everything that can be computerized and to finish this task in shortest time possible. Computers thus play an important role in our everyday life which is no more to be demonstrated. The performance of computers is continuously enhanced, but this development has it’s limits. Therefore, computer scientists try to design a completely new generation of information processing machines. The quantum computer could be part of this new generation. Although the theory of quantum computing is clearly understood, it has proven extremely difficult to physically realize a quantum computer of which the information-processing capability is known to be much greater than that of a corresponding classical computer. The use of Nuclear Magnetic Resonance (NMR) as a technology for the implementation of quantum computers is well recognized. However, both the “software” (quantum algorithms) as well as the “hardware” (the molecule) are required to achieve this purpose. But, for NMR quantum computers, the design, the synthesis as well as the characterization of suitable molecules are very challenging.
In relation to the concept of the spin chain design, a 13-qubit molecule (13C-labeled 12-fluorododecanal) has been developed in order to implement the quantum mirror experiments and the efficient transfer of encoded states along the spin chain. The complex spectral patterns (overlapped 1H and 13C NMR signals); the coincidence along with the strong coupling of carbon resonances of the molecule did not permit the direct use of the synthesized molecule for quantum computing experiments. Therefore, Lanthanide shift reagents (LSR) have been used in order to alter chemical shifts. The corresponding tests were performed with unlabeled 12-fluorododecanal and unlabeled 12-(triphenylmethoxy)dodecan-1-ol.
Besides the design and the synthesis of a molecule for spin chain quantum computing experiments, the spin-lattice (T1) and the spin-spin (T2) relaxation times of small organic molecules were measured in supercritical carbon dixiode (SC CO2) and compared to those obtained in common low viscosity NMR samples. Quantum computing experiments using longer pulse sequence blocks would have been implemented on the samples presenting an increase in the relaxation time T2 in supercritical carbon dioxide. But only a few cases fulfilling this requirement were observed.
Finally, a 3-qubit molecule which is very well suited for thermal state NMR quantum computing was developed and synthesized: 2-13C-labeled Diethyl 2-fluoromalonate. Using this compound, the complete quantum algorithm for the evaluation of the Jones Polynomial was experimentally implemented. The 3-qubit thermal state NMR quantum computer was capable of evaluating the Jones Polynomial of the link 6.2.3 for several nontrivial values within the domain of definition. An exponential speedup in comparison to classical computers was established. The obtained experimental results were in very good agreement with both the theoretical expectations and the simulations.
Density functional theory results for chemical shifts and spin-spin coupling constants are presented for compounds currently used in NMR quantum computing experiments. Specific design criteria were examined and numerical guidelines were assessed. Using a field strength of 7.0 T, protons require a coupling constant of 4 Hz with a chemical shift separation of 0.3 ppm, whereas carbon needs a coupling constant of 25 Hz for a chemical shift difference of 10 ppm, based on the minimal coupling approximation. Using these guidelines, it was determined that 2,3-dibromothiophene is limited to only two qubits; the three qubit system bromotrifluoroethene could be expanded to five qubits and the three qubit system 2,3-dibromopropanoic acid could also be used as a six qubit system. An examination of substituent effects showed that judiciously choosing specific groups could increase the number of available qubits by removing rotational degeneracies in addition to introducing specific conformational preferences that could increase (or decrease) the magnitude of the couplings. The introduction of one site of unsaturation can lead to a marked improvement in spectroscopic properties, even increasing the number of active nuclei.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
The enormous theoretical potential of Quantum Information Processing (QIP) is driving the pursuit for its practical realization by various physical techniques. Currently Nuclear Magnetic Resonance (NMR) has been the forerunner by demonstrating a majority of quantum algorithms. In NMR, spin systems consisting of coupled nuclear spins are utilized as qubits. In order to carry out QIP, a spin system has to meet two major requirements: (i) qubit addressability and (ii) mutual coupling among the qubits. It has been demonstrated that the magnitude of the mutual coupling among qubits can be increased by orienting the spin-systems in a liquid crystal matrix and utilizing the residual dipolar couplings. While utilizing residual dipolar couplings may be useful to increase the number of qubits, nuclei of same species (homonuclei) might become strongly coupled. In strongly coupled spin-systems, spins loose their individual identity of being qubits. We propose that even such strongly coupled spin-systems can be used for QIP and the qubit-manipulation can be achieved by transition-selective pulses. We demonstrate experimental preparation of pseudopure states, creation of maximally entangled states, implementation logic gates and implementation of Deutsch-Jozsa (DJ) algorithm in strongly coupled 2,3 and 4 spin systems. The energy levels of the strongly coupled 3 and 4 spin systems were obtained by using a Z-COSY experiment.
Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing.Quantum information processing promises to extend today's computing resources.Quantum computers, theoretically, could solve problems much more quickly than any classic computer.Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms.In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols.The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area.Therefore, nuclear spins are picked out as good candidates for quantum bits.In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10—30 qubits.