Research On Quantum Adiabatic Evolution For Solving Max-Cut

This paper mainly study that the accuracy of quantum adiabatic evolution algorithm decreases when solving the max-cut.We use project Q quantum programming architecture to write the solution program,and test four influence factors to propose an improved scheme for quantum adiabatic evolution algorithm.Program constructs an adiabatic quantum system,and makes the system quantum state from a simple state to the max-cut Hamiltonian ground state according to the quantum logic circuit,the ground state corresponds to a solution of max-cut.The algorithm finally outputs system quantum state,so an approximate solution is obtained,which will be judged whether optimal or not according to the expected.The adiabatic evolution of quantum system is simulated in a classic computer.The results show that the algorithm can give highly accurate optimal solution for the max-cut with 3,4,5,6,7,9,10 and11 vertices.But when solving the graph with 8,12 and 13 vertices,the algorithm accuracy is greatly reduced,and the output result is not likely the optimal solution.So we study evolution times,evolution path,Hamiltonian and coupling strength these four influence factors.By adjusting the parameters,the test results show that the first two factors can not improve the algorithm accuracy,and improved Hamiltonian is only partially effective.While the coupling strength is mapped to a relatively small area,the expected value change of the max-cut Hamiltonian can meet the requirements of the algorithm accuracy,so mapping coupling strength can be used as an improvement plan.A set of architecture,which includes classical computing and quantum computing,is designed for the low-temperature superconducting quantum computer according to available hardware equipment.The classic computing is a main control terminal controlling whole quantum computer operation,while the quantum computing is a cooperative processing terminal dealing with large-scale data computing.The instruction set of the architecture can also be divided into quantum and classical instruction.Due to the limitation of related technologies,the formed low-temperature superconducting quantum computer can only realize simple quantum logic gate operations.And the operation process of quantum adiabatic evolution algorithm on quantum computer in the future is also introduced.