The Study Of Quantum Computation And Quantum Circuit Synthesis Based On Quantum Computing Chips

Although research on quantum computing and quantum computer has made great progress,there are still many problems in the manufacture of quantum computing application.Quantum chip is a strong candidate for the future quantum computing system.Under current scientific and technological conditions,quantum chips are facing following situations: In the presence of noise,a small on-chip quantum computing device with a certain scale.Above conditions can be summarized as "noisy intermediate-scale quantum(NISQ)”.It is a big challenge for researchers to build reasonable architectures,control flows and quantum algorithms for noisy medium scale quantum condition,which has been highly concerned by industry and academia.Considering decoherence and noise in quantum computers,algorithms generating short depth circuits are crucial to the reduction of calculation errors in quantum computers.Quantum circuit synthesis is an efficient way to deduce the equivalent circuit of an algorithm.It allows the same quantum program to progress on different quantum computing devices.On the other hand,developers of quantum programs only need to pay attention to the design itself,they don't need to consider the underlying hardware details.It maintains the quantum computers' transparency as the classical computers.This paper presents a simulated annealing-based algorithm,which can compile any unitary transformation into a general quantum gate sequence specified in the quantum gate set of a quantum computing chip.Based on experience search theory and technology,the algorithm searches the solution space and optimizes with cost function(gradient descent)after formalizing the synthetic quantum circuit problem.After multiple iterations,a high-quality output circuit can be obtained from the algorithm.In this paper,we discuss the search strategy and cost function of quantum circuit synthesis problem in details.We use various techniques to expand the boundary of solutions to achieve approximate optimal solutions in polynomial time complexity.This paper provides a demonstration of topology-aware compilation algorithm,mainly considering implementations of quantum walks on quantum chips.We specifically show the method to relocate unitary transformations to quantum computing chip circuits with different functions through our proposed algorithm.We also study the distribution and convergence of quantum walks in this paper.We establish a quantum central limit theorem(QCLT)for discrete quantum walks and study the statistical hypothesis testing for the standard or decayed walker probability distribution for imperfect quantum walks based on the proposed QCLT.We could obtain a reliable statistical analysis result for the imperfect distribution in the experimental quantum walk study.In this paper,we consider the application of quantum walk algorithm on our synthesis algorithm,we also simulate the quantum walk on quantum chips and analyze its characteristics.To verify our main theories and algorithms proposed in this paper,under the objective conditions that current technologies do not support experiments on actual quantum platforms,we study two typical "cloud quantum computing platforms".We simulate the results of quantum circuit synthesis running on them.Our experimental results show that,compared with other technologies,our proposed algorithm achieves a good balance in circuit depth and running time(which can be changed with different parameters).For quantum computing devices with limited topology,experiments show that depths of synthesized circuits only increase moderately.In some cases,circuits obtained by our algorithm are better than other technologies,which shows that our proposed algorithm can deal well with limited-topology devices.Our research of quantum circuit synthesis and general quantum algorithms on quantum chips can provide more theoretical and technical reference for the designs of quantum computing chips and provide a good theoretical and technical basis for the evolution of quantum chip micro-structures,quantum programming languages and quantum compiling tool chains.