Magnetization of a spin1/2 set is determined by means of their individual wave function. The theoretical treatment based on the fundamental axioms of quantum mechanics and solving explicitly Schrödinger equation gives the evolution of spin1/2 system driven by magnetic fields. In this work we consider the energy of the spin system interacting with magnetic fields and all the other parts of the energy as a constant reservoir. Solving this complete Hamiltonian can explain the measured sign change of nuclear spin noise spectra compared to conventional NMR experiments and the possibility to make NMR images without radio frequency magnetic fields. The possibility to make NMR images without RF magnetic fields is an indication that entangled spin1/2 states can be manipulated by magnetic field gradients, opening a new way to perform quantum computation by NMR.
Magnetization of a spin1/2 set is determined by means of their individual wave function. The theoretical treatment based on the fundamental axioms of quantum mechanics and solving explicitly Schrödinger equation gives the evolution of spin1/2 system driven by magnetic fields. In this work we consider the energy of the spin system interacting with magnetic fields and all the other parts of the energy as a constant reservoir. Solving this complete Hamiltonian can explain the measured sign change of nuclear spin noise spectra compared to conventional NMR experiments and the possibility to make NMR images without radio frequency magnetic fields. The possibility to make NMR images without RF magnetic fields is an indication that entangled spin1/2 states can be manipulated by magnetic field gradients, opening a new way to perform quantum computation by NMR.
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.
Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
In NMR experiments, interaction of quantized radio-frequency (rf) field leads to entanglement of nuclear spin with the electromagnetic field. In an entangled state, the nuclear spins are depolarized with no net magnetization, which cannot give a detectable signal in inductive detection. We show that when the electromagnetic field is in coherent state, inductive detection is just true. We develop the mathematics to study the evolution of a coherent rf-field with a sample of all polarized spins. We show that evolution can be solved in closed form as a separable state of rf-field and spin ensemble, where spin ensemble evolves according to Bloch equations in an rf field. We extend the analysis and results to a spin ensemble with Boltzmann polarization. The rabi frequency and coupling strength of spins to rf-field depends on number state of the rf-field. We show that in interaction with a coherent rf-field, this variation in coupling strength, introduces negligible error.
In this article we have considered the effect of a magnetic field, the Zeeman effect, nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) on nuclei with spin S ½ looked.Then energy levels, transition frequencies and the energy spectra for the nuclear spins have specified.After using the group definition SU(2), SU(3), SU(4), SU(N) OR SU(2S+1), In quantum mechanics and quantum computation the range nuclear energy levels sin to one qubit, qutrit and qudit assign.We have defined the quantum states.
After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this high degree of randomness, it is possible to investigate QIP because the relaxation time (the time scale over which useful signal from a computation is lost) is sufficiently long. We explain how this feature leads to the crucial ability of simulating a pure (non-random) state by using ``pseudopure'' states. We discuss how the ``answer'' provided by a computation is obtained by measurement and how this measurement differs from the ideal, projective measurement of QIP. We then give implementations of some simple quantum algorithms with a typical experimental result. We conclude with a discussion of what we have learned from NMR QIP so far and what the prospects for future NMR QIP experiments are.
With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.