An approach towards approximation of the Design of Quantum Gate
Shakti Sharma, Harish Parthasarathy, Akash Tayal, Geeta Bhatt, Manoj Khanna and Updesh Sharma
Abstract
Quantum Gate is a Unitary operator or a Unitary Gate for evolution of a quantum operation which satisfies condition U-1=U*. Quantum gates are different from classical gates. Quantum gates are always reversible therefore energy loss does not occur between input and output states. Hadamard gate, Phase Gate, CNOT (Controlled NOT) Gate etc are quantum gates. Scattering technique is used to obtain information on the particles therefore applied for evolution. Several algorithms have been developed for quantum computers like Shor’s algorithm, Searching algorithms, Fourier transform algorithm. There are various hardware mechanisms are developing through which these gates are tried to be implemented like Ion traps, Quantum Dots, Impurity Atoms, Superconductors etc. In this paper an effort has been done to present a mathematical approach of quantum computer gate design using MATLAB. In this paper, a unitary gate Ud is realized using an atomic system under evolution having Hamiltonian H0. After time t, U0(t)=exp(-itH0). H0 is designed in a way so that U0(t) Ud. Then Ud got perturbed slightly to U’d=Ud+δUd and extensive efforts have been done to correct the atomic evolution operator U0(t) so that U’d is well approximated. For the purpose the atomic evolution theory has been followed by a time independent scattering process with a weak potential εV. Unitarity of evolution is defined by Quantum Fourier Transform algorithm which performs Fourier transform of quantum mechanical amplitudes.
Keyword
Born approximation, Quantum Computation, Quantum Fourier Transform, Quantum Gate, Unitary Gate, Perturbation.