Research On Quantum Computing Algorithms For NISQ Era

Although universal fault-tolerant quantum computers have unparalleled capabilities of classical computers in solving problems such as large integer prime factorization and unstructured database search,the technical solutions of achieving millions of qubits with a low error rate and long coherence time are not yet clear.The fault-tolerant quantum computing is not yet mature.It is impossible to accurately predict the development prospects of universal fault-tolerant quantum computers.However,quantum devices with 50 to hundreds noisy qubits,known as Noisy Intermediate-Scale Quantum(NISQ)devices,have been built.From now to the future,it will be in the NISQ era for a long period,which is a necessary stage in the transition to the faulttolerant quantum era.In the process of finding quantum advantages for NISQ devices in the NISQ era,quantum algorithms and their applications have also been innovatively developed.Quantum algorithms have been applied to many fields such as quantum chemistry,physics,machine learning,and combinatorial optimization,and achieved remarkable results.Despite the rapid development of quantum algorithms for the NISQ era,the challenges they face remain formidable.In this paper,some problems in quantum neural networks and in the optimization of quantum algorithm circuit implementation in the NISQ era are studied.The main contents are as follows:1)Quantum neural networks have great potential to surpass classical artificial neural networks,and various typical quantum neural network models have been developed.However,quantum neural networks are facing the challenge of how efficiently fusing nonlinear neural networks into linear,unitary quantum systems.This paper first points out that the quantum oracle based on the quantum phase estimation algorithm can calculate arbitrary functions,and then proposes a generalizable framework for realizing nonlinear quantum neurons.According to this framework,combined with controlled phase-shift gates and the SWAP test algorithm,two nonlinear quantum neurons based on qubit encoding and amplitude encoding are proposed respectively.This is also the first time that a quantum neuron capable of expressing arbitrary nonlinear activation functions requiring polynomial quantum resources has been proposed.Finally,the results of IBMQ and Hi Q quantum cloud platform experiments and local computer numerical simulations both verify the correctness and effectiveness of the proposed nonlinear quantum neuron.2)Theoretically,the HHL algorithm has an exponential acceleration effect in solving the linear equation system problem compared with the fastest classical algorithm.But the HHL algorithm is still a proof-of-concept algorithm,and its application to solve practical scientific and engineering problems requires substantial quantum resources.In particular,the controlled rotation module in the HHL algorithm has the problems of unclear and inefficient quantum circuit implementation,which seriously affects the fidelity and acceleration effect of the HHL algorithm.Based on quantum phase estimation,this paper proposes a general method for realizing controlled rotation modules in quantum algorithms,which can be applied to HHL algorithms and HHL-like algorithms.Numerical simulation results show that the proposed method only requires a small number of auxiliary qubits to ensure the high fidelity of the HHL algorithm.Compared with the polynomial fitting function method,within a certain error range,the method only needs fewer quantum gates to realize the controlled rotation module of the HHL algorithm.Furthermore,the gate complexity of this method is also polynomial if the corresponding diagonal unitary matrix can be decomposed efficiently.In this paper,the construction method of nonlinear quantum neurons and the realization method of controlled rotation modules of quantum algorithms are proposed,which can more fully demonstrate the superiority of quantum.Meanwhile,we offer useful reference for running quantum algorithms and quantum machine learning algorithms in the NISQ era with limited quantum resources.