Based on physical model of two-qubit quantum computer,two kinds of rules were proposed by solving single-body and two-body the time-dependent Schrdinger equation for designing nuclear magnetic resonance pulse sequence parameter of Grover quantum algorithm.Specified parameters were given through two kinds of designing rules and numerical simulations were carried out as specifying parameters.Results from the simulations show that target state is a pure basis state after running specified parameters by solving two-body the time-dependent Schrdinger equation and the expectation value of z-component of target state agrees with the theoretical values with a precision about 10-3.It is confirmed that rules of designing parameter is correct.
Based on physical model of two-qubit quantum computer,two kinds of rules were proposed by solving single-body and two-body the time-dependent Schrdinger equation for designing nuclear magnetic resonance pulse sequence parameter of Grover quantum algorithm.Specified parameters were given through two kinds of designing rules and numerical simulations were carried out as specifying parameters.Results from the simulations show that target state is a pure basis state after running specified parameters by solving two-body the time-dependent Schrdinger equation and the expectation value of z-component of target state agrees with the theoretical values with a precision about 10-3.It is confirmed that rules of designing parameter is correct.
We displayed the nuclear spin coupling and dipole polarisation in magnetic resonance microscopy based on quantum calculation. When radio frequency (rf) probing operated nuclear spins on the nanometer localisation, Grover’s quantum algorithm can be realised by polarisation enhanced states using pulse sequence and width according to the interaction between RF and spins. We theoretically proposed two-qubits quantum system of density matrix to achieve quantum Grover’s algorithm in spin damp and frequency shift based on magnetic resonance microscopy. The nuclear spins were operated by pulse time sequences of cyclic adiabatic inversion, and controlled the quantum spin magnetic moment state to achieve the superposition. The resonance spins excited by radio frequency coil and magnetic tip were measured by the nuclear magnetic moment, spectrum and density matrix. The results indicated that the density matrix was used to read out quantum spectrum image. Grover’s algorithm can perform search faster than their classical counterparts. The force microscopy properties of spin damp decay holds great promise of magnetic resonance in quantum computing, quantum communication. Theoretically the algorithm is accelerated but not 100% in a rate of success.
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.
Currently,the NMR technology is one of the effective physical systems to realize quantum computation.As the multiple-quantum operator algebra theory mentions,any unitary transformation can be decomposed into a sequence of a limited number of one-qubit quantum gates and two-qubit diagonal gates.Based on these backgrounds,we propose a method to form NMR pulse sequences to realize the multi-qubit Grover quantum search algorithm.Experiments finish the algorithm with three-qubit,on a Quantum Computer Emulator.
A continuous, analog version of the Grover algorithm is realized using NMR. The system studied is 23Na in a liquid-crystal medium. The presence of quadrupolar coupling makes the spin I=3/2 nucleus a two-qubit system. Applying a specially designed pulse sequence, the time evolution of the spin-density operator is described in an interaction representation that has no external time-dependent radio-frequency fields. This approach is used to implement one instance of the continuous Grover search for the transform of a uniform state to a target state, and the implementation provides a clear physical interpretation of the algorithm. The experimental results are in good agreement with the theory.
With the technique of opposite phases, the sequence pulse for exact controlled not gate was designed, and the controlled controlled phase shift gate, which is the key gate in Grovers algorithm, and the double controlled not gate were also constructed by employing only two body interaction. The symmetric operators of quantum states were made up. All the above are the tools of the quantum state engineering, therefore, theyare very useful for both theoretic and experimental investigations of quantum computation.
Quantum information processing is a multi-disciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum level, either for simulation of physical systems, or numerical computation. Although it has been known for almost a decade that a quantum computer would enable the solution of problems deemed infeasible classically, constructing one has been beyond today's capabilities. In this work we explore one proposed implementation of a quantum computer: Nuclear Magnetic Resonance (NMR) spectroscopy. We also develop a numerical software tool, a pulse sequence compiler, for use in the implementation of quantum computer programs on an NMR quantum computer. Our pulse sequence compiler takes as input the specifications of the molecule used as a quantum register, the desired quantum gate, and experimental data on the actual effects of RF pulses on a sample of the molecule, and outputs an optimum set of pre and post 'virtual' gates that minimize the error induced.