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This paper deals with the design of quantum unitary gate by matching the Hermitian generators. A given complicated quantum controlled gate is approximated by perturbing a simple quantum system with a small time-varying potential. The basic idea is to evaluate the generator $$H_\varphi $$ H φ of the perturbed system approximately using first-order perturbation theory in the interaction picture. $$H_\varphi $$ H φ depends on a modulating signal $$\varphi (t){:}\; 0\le t\le T$$ φ ( t ) : 0 ≤ t ≤ T which modulates a known potential V. The generator $$H_\varphi $$ H φ of the given gate $$U_\mathrm{g}$$ U g is evaluated using $$H_\mathrm{g}=\iota \log U_g$$ H g = ι log U g . The optimal modulating signal $$\varphi (t)$$ φ ( t ) is chosen so that $$\Vert H_g - H_\varphi \Vert $$ ‖ H g - H φ ‖ is a minimum. The simple quantum system chosen for our simulation is harmonic oscillator with charge perturbed by an electric field that is a constant in space but time varying and is controlled externally. This is used to approximate the controlled unitary gate obtained by perturbing the oscillator with an anharmonic term proportional to $$q^3$$ q 3 . Simulations results show significantly small noise-to-signal ratio. Finally, we discuss how the proposed method is particularly suitable for designing some commonly used unitary gates. Another example was chosen to illustrate this method of gate design is the ion-trap model.
Quantum Information Processing – Springer Journals
Published: Mar 15, 2017
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