The Research For Quantum Algorithm System And Its Application In Genetic Engineering

Focusing on the research and application of Quantum Algorithms,this paper was divided into three parts,which were the studying and Nuclear Magnetic Resonance(NMR) simulation of multi-qubit Quantum Algorithms;the design and analysis of classical coupled harmonic oscillators system which corresponded to Grover search algorithm;and,proposing the model of nucleotide base selection and H-bond formation in DNA replication and proteins synthesis,which corresponded to quantum information processing mechanism.In the first part,based on the operator approach,we proved the generalized Grover search algorithm completely.That is,in Grover iteration,the Walsh-Hadamard transformation could be replaced by an arbitrary unitary transformation,and the phase inversions could be replaced by arbitrary phase rotations.NMR has been considered as one of the most effective physical system to realize quantum computation.As multiple-quantum operator algebra theory mentioned,any unitary transformation can be decomposed into a sequence of a limited number of one-qubit quantum gates and 2-qubit diagonal gates.Based on multiple-quantum operator algebra theory,the Generalized Kronecker Product,Perfect Shuffle Permutation Matrices and Bit-Reversal Permutation Matrices,we proposed the method to design NMR pulse sequences to implement Generalized Quantum Search Algorithm with arbitrary phase rotation,Quantum Fourier Transform and Quantum Wavelet Transform.Meanwhile,we designed the pulse sequences for 2-qubit generalized and 3-qubit classical Grover algorithm, Quantum Fourier Transform,Quantum Harr and D⁽⁴⁾ Wavelet Transform.Then we experimental finished the algorithm with different phase rotations respectively in a 2-qubit system,on a Quantum Computer Emulator(QCE),and discussed the best phase rotating angle. Meanwhile,the 3-qubit classical Grover algorithm,2-,3- and 4-qubit Quantum Fourier Transform,3-qubit Quantum Harr and D⁽⁴⁾ Wavelet Transform were simulated on QCE.The difficulty of realizing multi-qubit quantum algorithm is to overcome the coupling effect within spins.Based on multiple-quantum operator algebra theory,those high dimensional unitary transformation,which expressing coupling within spins,could be decomposed into a sequence of one-qubit and 2-qubit basic quantum gates.Setting the specific phase rotating angle,the quantum gates could be converted into NMR pulse sequences.At the end, according to the classical and quantum coherence,through the density matrix of quantum state,the quantum coherence during the iteration of Grover searching was studied,and the relation between quantum coherence and the number of iterations was proposed.In the second part,we designed a macroscopic system with wave features,aimed to classical coupled harmonic oscillators system.Because of the physical conjunction to couple those small oscillators,the vibration of a oscillator around its equilibrium could be seemed as binary state of a qubit.Such classical wave system is far more stable against decoherence compared to its quantum counterpart.We analysized the dynamic mechanism,effective Hamiltonian,eigenvalues and the corresponding eigenmodes for the system.We proved that during the vibration,if one of those oscillators was given a elastic reflection,after few round vibrations,the energy of the system was concentrated to this oscillator,making it to the maximum energy.The oscillator was reached as the target for a unsorted search.Also,we found that when the energy of the target oscillator getting to the maximum,the times of vibration had a squarely relationship with the number of small oscillators.So Grover quantum search algorithm were proved to be physically implanted in such a macroscopic wave system.The nucleotide base-pairing in DNA replication and proteins synthesis,which were basic procedures in genetic information processing,could be looked upon as an unsorted database search..The legacy of Charles Darwin—survival of the fittest,has proved,from the point of biology,that genetic information processing is optimal.DNA replication and proteins synthesis are classical.Because of the disturbance from circumstances,it is hard for them to maintain quantum coherence.So it seems there were some unovercomed difficulties to describe them under pure quantum situation.Based on the classical coupled harmonic oscillators system,which corresponded to Grover quantum search algorithm,and quantum tunneling effect,the model of the nucleotide base selection and H-bond formation was proposed in the last part of this paper.In addition,the catalysis of the DNA and RNA polymerase was discussed from the point of view of quantum coherence maintained.Finally, we proved the optimization of biological information processing through the point of informatics.