Research On The Linear Optical Quantum Computing

Harnessing the intrinsic nature of quantum mechanics,quantum computers promise to provide an exponential speedup over their classical counterparts for certain tasks,which could be applied to the fields of cryptanalysis,nuclear explosion simulation,military meteorology,and machine learning.Thus,it is of great significance to study the realization techniques of quantum computing.In this paper,we focus on linear optical quantum computing,and systematically study the foundation,algorithm realization,and application mode of quantum computing.The main results are as follows:(1)In terms of the foundation research,the role of quantum resources in quantum-computational speedup,the preparation method of larger-scale photon qubits,and high-efficient quantum gates are studied,which could provide basic support for the implementation and application of quantum computing.1.Research on the accelerating effect of quantum entanglement in quantum computing.Studying the accelerating effect of different types of quantum resources in quantum computing could provide the guidance for designing new quantum algorithms.However,the effectiveness of quantum entanglement in quantum computing remains a question of debate.To study this issue,a Deutsch-like problem is designed,and we prove that the quantum algorithm without entanglement can not provide acceleration compared to the classical algorithm for this problem.However,if we use the entanglement,the quantum speedup can be obtained by designing a new quantum algorithm.Furthermore,experiments are implemented to demonstrate the proposed quantum algorithms.For the first time,our results clearly show that for certain problems,quantum entanglement is a necessary resource for quantum acceleration in quantum computing,providing reliable and clear guidance for the further design of new quantum algorithms.In addition,our proposed quantum algorithm can be directly used to study the properties of Boolean functions,which could be applied to the cryptanalysis based on Walsh spectrum.2.Research on photon qubits preparation and deterministic Toffoli gate.Quantum bits and quantum gates are the basic elements of quantum computing.Therefore,it is the primary task to prepare more quantum bits,and design high-efficient quantum gate.To prepare more photon qubits,we develop the techniques of high-quality entangled photon source and three degrees-of-freedom manipulation,and then successfully realize the preparations of ten-photon entangled state and 18-qubit entangled state,which are the new records in the linear optical quantum computing.In addition,basing on the three degrees-of-freedom of single photon,we first propose a deterministic implementation scheme of Toffoli gate for the linear optical quantum computing,and analyze the actual performance of the scheme,providing a basic quantum gate operation for high-efficient linear optical quantum computing.(2)In terms of the algorithm realization,the realization methods and verification methods for universal-type and non-universal-type quantum computations are studied respectively,which could provide more ideas for solving practical problems by using quantum computing.1.Demonstration of quantum topological data analysis.By extracting the key modules in the quantum topological data analysis algorithm and introducing some equivalent transformations,we design a 5-qubits simplified quantum circuit for the quantum topological data analysis algorithm.Then,a proof-of-principle experiment is implemented to demonstrate this quantum circuit by employing a six-photon quantum processor.In the experiment,to ensure the reliability of results,we develop the manipulation techniques of ultra-high-fidelity 3-qubits mixed state and entangled state,and successfully analyze the topological features of Betti numbers of a network including three data points,providing new insights into data analysis in the era of quantum computing.2.Research on the verification method for collision-free Boson Sampling.Since the Boson Sampling is mathematically difficult for classcial computer,how to verify the results becomes a huge challenge for Boson Sampling experiments.By analyzing the two mode correlation function,we develop a statistical analysis scheme to verify the collision-free Boson Sampling.Numerical simulations show that our proposed scheme is very feasible and practical.Furthermore,By developing high-quality single-photon source and super-low-loss bulk interferometer,we realize a high sampling rate three-photon collision-free Boson Sampling.The sampling rate of the Boson Sampler was 636 Hz,which was several thousand times higher than the previous experiments.By analyzing the two mode correlation function,the output of the three-photon collision-free Boson Sampling is successfully verified.The verification method and the techniques developed in the experiment could lay the foundation for realizing large-scale Boson Sampling and demonstrating the "Quantum supremacy".(3)In terms of the application model,several types of cloud quantum computing protocols are studied,which lay the foundation for future secure cloud quantum computing.1.Experimental secure cloud quantum computing for a classical client.The secure cloud quantum computing aims to share the power of quantum computing resources while protecting the privacy of clients' data.However,all the secure cloud quantum computing experiments so far require clients to have weak quantum devices,which limits the widespread use of cloud quantum computing.Here,we implement a proof-of-principle experiment for completely classical clients.By interacting with two quantum servers that share entanglement using RUV protocol,the client successfully let the quantum servers factorize N=15 while protecting the privacy of his data.Our demonstration shows the feasibility of secure cloud quantum computing for completely classical clients and thus is a key milestone towards secure cloud quantum computing.In addition,the realization of Shor algorithm on cloud quantum servers shows the possible of using cloud quantum servers for cryptanalysis.2.Research on secure cloud quantum computing on various cloud platforms.There are many possible types of cloud quantum platforms in the future.Here,we consider two types of cloud quantum platforms,and give the corresponding schemes for secure cloud quantum computing: 1)Secure cloud quantum computing for hybrid systems.Through employing the method of entangling different physical systems to realize the transmission of encrypted quantum qubits,we design a secure cloud quantum computing protocol for hybrid quantum system,and analyze its security,correctness and scalability.The protocol could be used as framework and can be further enhanced by adapting other protocols to the framework.2)Secure cloud quantum computing for the existing cloud quantum platforms.Based on the idea of homomorphic encryption,a classical encryption protocol for HHL algorithm is designed.The fusion method of “classical encryption + quantum algorithm” could provide a feasible idea for future secure cloud quantum computing.Furthermore,we successfully implement HHL algorithm on IBM's cloud quantum computer platform while protecting our privacy by using the proposed protocol,which is the first secure cloud quantum computing on the existing cloud quantum platforms.