Reducing the effect of noise on quantum gate design by linear filtering

In this paper, we discuss how to reduce the interference that noise introduces into the scalar input signal of a quantum gate. Non-separable quantum gates can be made by making a small potential change to the Hamiltonian and then using perturbation theory to figure out the evolution operator. It is assumed that a scalar, temporally varying signal modulates the potential. To lessen the impact of noise on the design of the gate, we here take into account an extra noise component in the input signal and process it with a linear time-invariant filter. In order to meet these requirements, the Frobenius norm of the difference between the realized gate and the theoretical gate is minimized while taking into account the energy of the signal and the energy of the filter. Results from a computer simulation have been obtained by discretizing the resulting equations. The simulation results show that the proposed method effectively reduces the impact of noise on the gate design and improves its performance. This approach can be useful in designing gates for various applications, including signal processing and communication systems.