Implementation And Optimization Of Two Degrees Of Freedom Hyper-parallel And Efficient Optical Quantum Computation

Quantum computing is a model of measuring and controlling quantum information units based on the principles of quantum mechanics and performs super-fast calculations.Currently,quantum computing is one of the core research areas in "quantum information and precision measurement" and has been listed as one of the key frontier research areas in China’s national science and technology innovation plan for the 14 th Five-Year period,with extremely high academic,commercial,and military value.The core task of quantum computing is to achieve the most efficient quantum logic gate with the least quantum resources.The use of a multidegree-of-freedom(Do F)ultra-parallel quantum computing model,which simultaneously performs parallel computing operations on multiple degrees of freedom of the photon system,has the advantages of simplifying quantum computing circuits,improving quantum computing speed,and saving quantum resources.This master’s thesis mainly focuses on the implementation and optimization of the two degree-of-freedom hyper-parallel efficient optical quantum computing,and has achieved some significant research results:Based on the quantum state selective reflection nature of the microcavity solid-state system,we have designed a fault-tolerant hyper-parallel three-photon Toffoli gate between polarization and spatial Do Fs.It is equivalent to the cascade of two single-Do F(polarized or spatial)Toffoli gates acting simultaneously.It has the advantages of increasing quantum operations,saving quantum resources and suppressing photon scattering noise.It has important applications in the generation and analysis of super-entangled states.In addition,in the whole operation process of the model,two photons are transmitted in reverse direction,which greatly saves the operation time.Furthermore,using the existing experimental technology,the model can realize fast and sensitive quantum operation even under weak coupling conditions.The synthesis of traditional single-Do F Toffoli gate requires 12 CNOT gates,while our schemes require half of the quantum resources,and is immune to manipulation induced by imperfect parameters,with a theoretical fidelity of 100%.In addition,because the modular circuit of the hyper-parallel Toffoli gate we built has high flexibility,it can be directly used to build three types of hybrid hyper-parallel Toffoli gates,which have the same fidelity and efficiency as the hyper-parallel Toffoli gates.Therefore,it is expected to realize hyper-parallel module for multi-bit quantum computing.Based on the two-photon polarization-SWAP(P-SWAP)gate constructed by the Λ-type three-level atomic cavity system,we have designed a two-photon hyper-parallel CNOT gate and a three-photon hyper-parallel Toffoli gate on two Do Fs,which can be realized by two and four P-SWAP gates that below the theoretical lower limit.In addition,these two-qubit gate can be flexibly extended to(m+1)photons and(n+1)photons.Only 4m and 4n P-SWAP gates can be used to construct a 2m-target-qubit hyper-parallel CNOT gat and a 2n-control-qubit hyperparallel Toffoli gate,which greatly reduces the cost of constructing a multi-qubit logic gate and bridges the gap between the theoretical lower limit of optical quantum computing and the optimal synthesis.In addition,the only auxiliary atom for constructing the quantum gate does not need to be initialized and measured,because the state of the atom remains unchanged after the completion of the hyper-parallel quantum computing.Overall,it is only used as a temporary quantum memory,that means it can be reused in the coherent time.Also based on the principle of interaction between a single photon and a Λ-type three-level atomic cavity system,we propose some schemes to realize CNOT,Fredkin and Toffoli gates using hybrid system.The first control qubit of these quantum logic gates is encoded on a single photon,and the rest qubits are encoded on atom-cavity systems.In addition,these quantum gates can be extended to the best high-dimensional multi-qubit CNOT,Fredkin and Toffoli gates.These quantum logic gates only need O(n)linear optical components,and do not need auxiliary photons or atoms.These simple single-qubit operations are only applied to the photon through optical components,which makes these logic gates experimentally feasible under the current technology.