Research On Several Issues In Quantum Computation And Quantum Information

Quantum computation and quantum information, as an interdisciplinary combined with quantum mechanics, computer science, information theory, cryptography, and many other disciplines, has been developed rapidly. The microscopic characteristics of quantum are mainly reflected in: quantum decoherence, entanglement, superposition, and quantum no-cloning theorem. These characteristics determine that the physical realization of quantum computation and quantum information is very difficult. Researchers have made plenty of work about physical implementation of quantum logic gates and physical transmission of entanglement, such as, cold trap bound ions, and so on. Construction and implementation of universal quantum logic gates are necessary conditions for the implementation of quantum computation and quantum computer. Quantum entanglement is the most important resource and the key research subject of quantum information. Meanwhile, it plays a fundamental role in quantum teleportation, quantum key distribution and quantum correction. Combined with the integrated information and attractors, quantum information entropy broadens the practical application of quantum theory further.It mainly studies quantum logic circuit synthesis, construction of quantum increment gate, the criterion of quantum entanglement, the relationship and application of quantum entropy and other disciplines. The details of the research work and innovations are as following:1. Quantum logic circuits synthesisBased on the group theory, it innovatively presents four logic circuits synthesis algorithms with minimum quantum cost. These four algorithms are used to resolve the problem of minimum length and minimum quantum cost of logic synthesis. These algorithms transform quantum reversible logic circuits into the permutation group representation, and combine with GAP software to exactly synthesize three qubits quantum reversible logic circuits. Experimental results show that the logic synthesis ability of Peres gate is better than Toffoli gate.2. Quantum ternary logic synthesis and hybrid-logic synthesisCombined with the methods of classical logic circuits synthesis creatively, the irreversible logic can be transformed into a reversible logic. Then, it is extended to the issue of ternary logic synthesis. Based on the SNT gate library, it presents a synthesis algorithm called STNC, which uses minimum qutrits. This method has been proved that it is efficient to synthesize any three inputs irreversible logic circuits. For synthesizing a certain hybrid-logic 5-qubit quantum logic circuits, a new quantum logic gate AHX is proposed and constructed. Furthermore, it verifies synthesis ability of AHX logic gate and CNOT gate in synthesizing Toffoli gate according to the bi-search algorithm.3. The construction and application of quantum increment gatesIt proposes a class of quantum increment gates innovatively, including three topological types(N: 0),(N: N-1: RE) and(N: N-1: RD). Meanwhile, it gives analysis and comparison among three increment gates, from the number of ancilla qubits, circuits complexity, the type of used basic logic gates, the number of basic logic gates, the total number of used logic gates, etc. Although the basic quantum increment gate does not use ancilla qubits, its circuit complexity is tremendous. The rest two cases use full ancilla qubits to reduce the circuit complexity. However, it increases the requirement of quantum registers. In addition, for the basic quantum increment gate, it also gives two applications: quantum walk and quantum fan-out circuits.4. Relationship between quantum gate operations and quantum entanglementIt studies the relationship between quantum gate operations and quantum entanglement further. It analyzes the ability of basic quantum logic gates generating quantum entanglement. It also studies the ability of quantum increment gates producing entanglement. Three criterias(U)CK,(U)EK?and0(U, C)CK are listed to evaluate the ability of different quantum logic gate operation generating quantum entanglement.5. An entanglement measurement for arbitrary n-qubit quantum systemIt proposes a hierarchical entanglement measurement for arbitrary n-qubit quantum system creatively. It defines three conceptions to measure quantum entanglement, including the minimum entanglement measurement1,,lq qE, the average entanglement measurementavgE, and the maximum entanglement measurementmaxE. This method has no limitation of the number of qubits in a quantum system for entanglement measurement. Therefore, this method has a wider application value. At last, it gives the definitions of quantum effective information, mutual information and integrated information based on quantum information entropy. Meanwhile, it also gives a good insight of the application of quantum entropy in material science and others.