Researches Of Some Fundamental Topics In Quantum Computation

Quantum information is the perfect combination of quantum mechanics and modern information science. Quantum information processing technology already has attracted great attention from scientific community and become a hot research topic. Quantum information processing technology includes quantum communication technology and quantum computation. In contrast to the boom in the field of quantum communication, quantum computation, whose main research goal is to realize quantum computers, develops relatively slow. Although the quantum computer outperforms the classical computer for certain computational problems due to quantum properties, it remains a huge challenge for experimental implementations. There are two ways to solve this problem for quantum computation. The first way is to optimize quantum algorithms and design reasonable physical implementation scheme; the second way is to improve the experimental technology. Among numerous physical implementation systems, the photon system has its unique advantages. Polarization and path, as the two degrees of freedom of photons, are natural quantum quibits which is easily manipulated; the photon system has long decoherence time and strong robustness; as fly qubits, photons have long transmission distance and high transmission speed. Depending on these advantages, the photon system is always the research hotspot in quantum physics and will play an important role for quantum computer and quantum communication technology in the future.This thesis carefully analyzes several fundamental issues in quantum computation and designs more reasonable algorithms and schemes. In addition, this thesis proposes relevant optical implementation schemes using the linear optical system and cavity quantum electrodynamics (QED) system. The main results are listed below.1. This thesis proposes a scheme for optimizing the two-qubit and three-qubit quantum circuits via using auxiliary Hilbert spaces. The scheme provides a theory and physical implementation way to reduce the complexity of universal quantum logic circuits. Utilizing the dimensionality of photon paths, two-valued logic qubits are extended to be four-valued logic ququart. Therefore, controlled operations between two qubits are converted to be unitary operations on single ququart. Combining the auxiliary dimensionality with cosine-sine decomposition (CSD) and quantum Shannon decomposition (QSD), the complexity of the two-qubit and three-qubit quantum circuit is reduced to be 4 CNOTs and 16 CNOTs, respectively. With the increase of the number of qubits, the advantage of the scheme will become increasingly prominent. This thesis designs the optical implementation based on linear optical elements and cavity QED system, providing a new method to build universal quantum circuits.2. This thesis proposes an optical scheme to perform measurement-based quantum computation using two-dimensional AKLT states. In the scheme, entangled photon pairs are generated via spontaneous parametric down conversion. After performing post-selection measurements on three photons generated by interference occurring on linear optical elements, the elementary unit of the two-dimensional AKLT state can be obtained. CNOT gates can be probabilistically implemented via performing projective measurements on neighbouring units. This scheme provides a new way to implement universal quantum computation.3. This thesis proposes a scheme for generation of NOON states via the cavity QED system. In the scheme, a double A-type three-level atom is trapped in a high-quality bimodal cavity. Driving the Raman transition of the atom by the classical optical field, nonclassical entangled states of one atom and N photons can be obtained after a series of operations and suitable interaction time. Then it can be converted to purely photonic NOON states by applying a single projective measurement on the atom. In this scheme, atomic spontaneous decay can be neglected due to the detuning of the cavity mode and classical pulse from the atomic excited state. Thus the scheme can effectively avoid decoherence and generate high photon number NOON states with high successful probability and fidelity.4. This thesis proposes a simple and effective scheme to distinguish the boson sampling with identical photons from the semi-classical mean-field sampling. Inputting the specific testing state, this scheme can identify the boson sampler and the mean-field sampler of any unknown unitary evolution without changing the structure of samplers. It demonstrates that the quantum computer has an advantage over the classical computer for solving the boson sampling problem. For the partial distinguishability induced by the mutual delay of injected photons due to the inaccuracy of light source, this thesis verifies the strong robustness of the scheme by simulation. This scheme remains valid to discriminate the partially distinguishable boson sampling and the mean-field sampling.This thesis optimizes the universal quantum circuit and measurement-based quantum computation. Then it proposes feasible optical implementation schemes of the linear optical system and cavity QED system. In addition, it proposes schemes for the generation of the NOON state and the certification of the boson sampling. These schemes have positive significance to optimize quantum algorithms and reduce the difficulty for optical implementation of quantum computation.