開放量子系統下量子邏輯閘的最佳化控制

黃琮暐

doi:10.6342/NTU.2009.03219

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開放量子系統下量子邏輯閘的最佳化控制

Optimal Control of Quantum Gate Operations in Open Quantum Systems

黃琮暐 , Masters　　Advisor：管希聖　　

英文 DOI： 10.6342/NTU.2009.03219

最佳化控制；量子邏輯閘；開放量子系統； Optimal control ； Quantum gate ； Open quantum systems

Abstract │ Reference (13) │ Altmetrics

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One of the important criteria for physical implementation of a practical quantum computer is to have a universal set of quantum gates with operation times much faster than the relevant decoherence time of the quantum computer. In addition, high-fidelity quantum gates to meet the error threshold are also desired for fault-tolerant quantum computation. So the main purpose of his thesis is to focus on finding control parameter sequence in near time-optimal way using an optimization approach, the Krotov method, for high-fidelity quantum gates in the Kane silicon-based donor spin quantum computer architecture where the donor electron
spins are defined as quantum bits (qubits). We first review the basics of silicon-based donor spin quantum computer proposed by Kane, and how to control the system and construct the quantum gates, including Hadamard gate, CNOT gate and so on, in canonical gate decomposition ways. We then introduce the Krotov optimization method which is one of the most effective and universal computation methods for
solving optimal control problems with a large dimension of state vectors. The Krotov method is then applied to find the optimal control sequence of a Hadamard gate in the Kane quantum donor electron spin computer. Quantum decoherece is still a major obstacle for the implementation of a pratical quantum computer. We then consider a decoherence model, derive a corresponding quantum master equation of the reduced density matrix of the qubits, and construct equations of motion for quantum gate evolution in the presence of external (thermal) environments. Finally, we apply the Krotov method to find optimal control sequence for Hadmard gate operation under the influence of external environments.

Reference ( 13 ) 〈TOP〉

[1] D.Deutsch. Quantum Theory, the Church-Turing thesis and the Universal Quantum Computer. Proc. Royal Soc. of London A400, 97(1985).
連結：
[2] B.E. Kane. A Silicon-Based Nuclear Spin Quantum Computer. Nature 393, 133(1998).
連結：
[4] C. Herring and Flicker, ”Asymptotic Exchange Coupling of two Hydrogen Atom”, Phys. Rev. 134, A362-A366(1964).
連結：
[5] V.F. Krotov, Global Methods in Optimal Control Theroy(Dekker,New York,1996)
連結：
[6] A.I. Konnov and V.F. Krotov, Automation and Remote Control Vol. 60, No. 10, 1999
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