Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation
نویسندگان
چکیده
The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a k-dimensional unitary gate which operates on an N -dimensional Hilbert space with N ≥ 2k. Our construction is applied to several important unitary gates such as the Hadamard gate, the CNOT gate, and the two-qubit discrete Fourier transformation gate. Controllers for these gates are explicitly constructed.
منابع مشابه
Isoholonomic Problem and Holonomic Quantum Computation
Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic problem in a homogeneous fiber bundle is formulated and solved completely. [Proceedings of International Conference on Topology in Ordered Phases organized by ...
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