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.
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.
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.
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.
Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a two-qubit Grover search using a molecule (13C 1HCl3) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.
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.
Liquid crystals offer several advantages as solvents for molecules used for NMR quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a 2-qubit Grover search using a molecule (13C1HCl3) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.
Quantum computation offers the extraordinary promise of solving mathematical and physical problems which are simply beyond the reach of classical computers. However, the experimental realization of quantum computers is extremely challenging, because of the need to initialize, manipulate and measure the state of a set of coupled quantum systems while maintaining fragile quantum coherence. In this thesis work, we have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of experiments which culminated in the implementation of the simplest instance of Shor’s quantum algorithm for prime factorization (15 = 3 × 5), using a seven-spin molecule. This algorithm achieves an exponential advantage over the best known classical factoring algorithms and its implementation represents a milestone in the experimental exploration of quantum computation. These remarkable successes have been made possible by the synthesis of suitable molecules and the development of many novel techniques for initialization, coherent control and readout of the state of multiple coupled nuclear spins. Furthermore, we devised and implemented a model to simulate both unitary and decoherence processes in these systems, in order to study and quantify the impact of various technological as well as fundamental sources of errors. In summary, this work has given us a much needed practical appreciation of what it takes to build a quantum computer. Furthermore, while liquid NMR quantum computing has well-understood scaling limitations, many of the techniques that originated from this research may find use in other, perhaps more scalable quantum computer implementations.