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Optimized Construction And Realization Of Quantum Circuits In Quantum Information Processing

Posted on:2013-11-06Degree:DoctorType:Dissertation
Country:ChinaCandidate:W D LiFull Text:PDF
GTID:1228330377952935Subject:Detection and processing of marine information
Abstract/Summary:PDF Full Text Request
In the20th century, people have come into the age of information because of therapid development of information technology. Now we can not imagine what the life islike without mobile phones and computers. At the same time, the development ofmodern technology, such as new material, biotechnology, medical science, andspaceflight, relys on the high-quality communication and computation technology, andthe requirement increases day by day. The development of the information processingtechnology depends to a large extent on the increase of the integration of the logic gatesand circuits. That means, the electronic device will become smaller and smaller. When itonly contains several atoms, the physical states of the device are difficult to be appliedin the traditional technology of information. At this time, the new quantum informationtheory based on quantum mechanics may become the new information platform, andquantum information processing technology may replace today’s technology.Along with the practical application of quantum cryptography and the start ofinternational quantum chip projects in recent years, quantum information processingtechnology gradually comes into the stage of collectively tackling key problems fromthe initial starting stage. Generally, the task of quantum information processing isrealized by executing the quantum circuits composed of elementary quantum logic gates,and the efficiency of the process is determined by the complexity of the quantumcircuits. However, the optimal construction of quantum circuits is still a unsolvedfundamental problem in quantum information processing currently.To obtain more efficient and simplified quantum circuits, we present optimalconstruction method focusing on specifical quantum communication and universalquantum computation problems, and obtain the optimal quantum circuits in this thesis. For entanglement concentration problem in quantum communication, we propose a newquantum circuit construction method based on state decomposition, by which theoptimal quantum circuit and physical realization scheme in optical systems fordeterministic entanglement concentration are obtained. For universal quantumcomputation, we present a new elementary quantum logic gate for4-level ququartsystems, and obtain a up-to-now optimal universal quantum circuit by using the newgate and QSD matrix decomposition method. Furthermore, we obtain a currentlyoptimal universal quantum circuit in qubit systems by applying the outcomes of ququartsystems to the qubit systems with extended Hilbert spaces. In detail, the main outcomesof our research are introduced as follows.1. To solve the problem that earlier universal quantum circuit construction method,such as the matrix decomposition method, can not effectively construct the quantumcircuit for specific problem in quantum information processing, we present thestate-decomposition quantum circuit construction method, which is given in theexample of deterministic entanglement concentration. In this method, the evolutionfrom the initial state to final state, corresponding to the specific problem, is divided intoseveral steps, then the whole quantum circuit is constructed by combining quantumcircuits constructed in every step. Compared with the matrix decomposition methods,this method is convenient for a large class of quantum processes involving generalizedmeasurements, such as the deterministic entanglement concentration and quantumtelepotation.2. A scheme for optimal deterministic entanglement concentration is proposed,and its corresponding quantum circuit and optical realization is presented by using thestate-decomposition method. In this scheme, the unitary evolution and quantum circuitfor deterministic entanglement concentration is optimal, as it requires the minimumancillary dimensions and the number of unitary operations. Moreover, we show that, byintroducing a path-polarization entanglement state based on the direct sum extension method, three elementary controlled phase-flip gates between two photons are sufficientin the design of its optical realization scheme, making it easy to be implemented fromthe experimental point of view. Meanwhile, the scheme is verified effective to recoverhighly entangled pairs from mixed states.3. We present a new method for constructing universal quantum circuit in ququartsystems and obtain the currently optimal universal quantum circuit. Here, a novelelementary two-ququart gate, termed controlled-double-NOT gate (similar to the CNOTgate in qubit systems), is proposed and its physical implementation is illustrated incavity-assisted linear optical systems, where the complexity is the same as the CNOTgate. Based on the proposed gate and QSD method, the optimal universal quantumcircuit in ququart systems is constructed.4. We present a new method for constructing universal quantum circuit in qubitsystems with the help of high-dimensions and obtain the currently optimal universalquantum circuit. Here, some qubits are converted into ququarts by using auxiliary2-dimensions. Then the universal quantum circuit in qubit systems is simplified byemploying the outcomes of ququart systems. As a result, we achieve the universalquantum circuit in qubit systems with the up-to-now lowest complexity.
Keywords/Search Tags:Universal quantum circuit, Entanglement concentration, High-dimensional quantum computation, Quantum circuit complexity, Auxiliary dimensions
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