Research On Synthesis Of Three-Valued Quantum Reversible Circuit And Three-Valued Quantum Algorithm

In the process of social progress, scientific and technological developments put forward higher requirements of the computing power and computer data processing efficiency. The three-valued quantum reversible logic circuit synthesis and the three-valued quantum algorithm proposed in this dissertation are the fundamental research to construct the next generation of quantum computer with faster computing speed.This dissertation analyzes the advantages of the three-valued quantum logic, and provides theoretical support for the study of three-valued quantum reversible logic circuit synthesis and three-valued quantum genetic algorithm. Then form the three-valued Pauli operator, after rigorous mathematical derivation, we define a set of fundamental three-valued quantum logic gates. By a number of lemma and theorem proving, we obtain the synthesis algorithm of ground state three-valued quantum reversible circuits, and design several typical three-valued quantum reversible logic circuits. The Cartan decomposition algorithm based on Lie group is also proposed, so the decomposition of arbitrary three-valued quantum unitary transformation is realized, and then arbitrary three-valued quantum reversible logic circuit synthesis is achieved.In this dissertation, we have proved that for any two different assigned vectors s and t, the exchange operation （ s t） can be implemented by a series of cascade EQKCXi gate. For arbitrary EQKCXi gate, we can use theiX gate and the QKCXi gate to achieve. All the ground state three-valued quantum reversible logic circuits can be implemented byiX gate and QKCXi gates. Based on these conclusions, the algorithm of synthesizing any arbitraryn′n ground state three-valued quantum reversible logic circuits is obtained.To further simplify and reduce the circuit, we define the QSwap gate, the QCNOT gate and the EQCNOT gate, and prove that all of the ground state quantum reversible logic circuit can be syntheized by 2-qutrit QSwap gate, QNOT and QCNOT gate, and without any additional bit. We also demonstrate that arbitrary ground state three-valued quantum reversible logic circuits can be synthesized by iX gate and 2-qutrit QCNOT gate.Cartan decomposition method based Lie group is introduced, and the arbitrary unitary gate acting on any single qutrit is decomposed into the form of e^iαR_y⁰¹（β）⁰²（γ）R_y⁰¹（δ）R_z⁰²（θ）R_z⁰²（φ）R_y⁰¹（β’）R_y⁰²（γ’）R_y⁰¹（δ’）, so the problem can be solved by transforming it into the product of several rotation gates of two ground state components. The U operator in 3nN = dimensional Hilbert space is decomposed into the form of U=（Σ|N）k=1e^iΨk|Ψ_k＞＜Ψ_k|=U₁U₂...U_N, thus the synthesis of any n-qutrit three-valued quantum reversible logic circuit is realized, and the correctness of the algorithm is verified through the complete synthesis of an 8-qutrit quantum reversible logic adder QT8 S.In terms of the three-valued quantum algorithms, the quantum Fourier transform is deeply studied in this dissertation, and then through rigorous mathematical derivation, the quantum Fourier transform is transformed into the form of tensor product of three-valued quantum state space. The three-valued quantum Hadamard gate and three-valued CRk gate are defined, and the three-valued quantum Fourier transform operation is achieved by them. The correctness of the three-valued quantum Fourier transform circuit is verified via a relatively simple case study. Through qualitative analysis, we find that when QFT algorithms is achieved with three-valued basic quantum gates, the number of quantum gates needed is about 50% of the binary quantum case, which further demonstrates the great advantage of three-valued quantum logic.In the research of the practicability of multi-value quantum algorithms, this dissertation combines the three-valued quantum computation principles and the genetic algorithms to design a three-valued quantum genetic algorithm, introduces three-valued qubits（qutrit） vector, and uses three-valued quantum rotation gate to realize the evolution of chromosome, resulting in a search algorithm which is better than the ordinary genetic algorithm. In order to verify the problem solving ability of three-valued quantum genetic algorithm, it is adopted in the wireless video sensor node deployment in Smart City. The simulation results show that the performance of the algorithm is outstading, and can meet the needs of engineering applications.