Research And Realization Of New Quantum Logic Gate On Construction Method

A quantum computer can be regarded as a quantum Turing machine.A quantum Turing machine is also equivalent to a quantum logic circuit,which is the mainstream model of quantum information.With the rapid development of quantum information,quantum circuits become more and more complex,the related theory and methods of automatic and efficient quantum circuit designs have been highly concerned.Since quantum circuits are composed of various kinds of quantum gates,which are the basis of quantum computation,so the optimization of quantum gates will directly affect the optimization of quantum logic circuits.Quantum gates can be divided into quantum non-logic gates and quantum logic gates.Compared with quantum logic gates,Since the quantum non-logic gates can synthesize better quantum circuits,synthesis of quantum non-logic gates have been the focus of research.Although many algorithms have been proposed,the vast majority of the synthesis algorithm has many obvious deficiencies.By discovery of constructing new quantum logic gates,we can avoid the direct use of quantum non-logic gates,which can simplify the problem into quantum logic problem,so as to optimize the overall quantum circuits.Therefore this paper conducted in-depth research on the related theory of quantum non-logic gate constructing new quantum logic gates,the main research work and results are as follows:(1)Quantum circuit synthesis using a new quantum logic gate library of NCV quantum gates is proposed.Since Controlled-Square-Root-of-NOT(CV,CV(?))gates are not permutative quantum gates,many existing methods cannot effectively synthesize optimal 3-qubit circuits directly using the NOT gate,CNOT gate and Controlled-Square-Root-of-NOT quantum gate library(NCV),and the key of effective methods is the mapping of NCV gates to four-valued quantum gates.Firstly,we use NCV gate library to create the new quantum logic gate library,which can be directly used to get the solutions with smaller quantum costs efficiently.Further,we present a novel generic method which quickly and directly constructs this new optimal quantum logic gate library using CNOT and Controlled-Square-Root-of-NOT gates.Finally,we present several encouraging experiments using these new permutative gates,and give a careful analysis of the method,which introduces a new idea to quantum circuit synthesis.(2)A common algorithm of constructing a new quantum logic gate for exact minimization of quantum circuits is proposed.Since non-permutative quantum gates have more complex rules than permutative quantum gates,direct use of non-permutative quantum gates should be avoided in the efficient synthesis algorithm because it is very hard to synthesize.The key method is using quantum gates to create new permutative quantum gates to replace non-permutative quantum gates.In this paper,we propose an algorithm using CNOT and non-permutative quantum gates to construct new optimal quantum logic gates library automatically.Our method based on the idea of exhaustion finds the all combinations of quantum logic gates with lower quantum cost no matter how many the quantum lines are.The idea of our algorithm and the experimental results are given in details.