Design and Realization of Quantum based Digital Integrator

Quantum mechanics is an excellent technique to counter and study the effect of noise in any system. A digital integrator can be designed with the help of quantum mechanics by passing a known signal ( ) to a known digital integrator, with impulse response ( ) and then, the output of this integrator ( ) is given to the input of a known quantum system (specified by its Hamiltonian ( ), perturbation parameter (ε), wave function (ψ) and a potential ( )) gives an output ( + 1). Now the same known signal is passed through an unknown FIR filter, which is to be designed and having impulse response h( ), and output of this FIR filter ( ) is again passed through the similar quantum system, which produce the output ( + 1). Then the coefficients of the unknown filter have been calculated by minimizing the Frobenius norm‖ ( )‖ , where [ , ( ) = ( + 1) − ( + 1)] and differentiating it with respect to the unknown FIR filter’s coefficients and by using adaptive algorithm. Thereafter the magnitude and phase of given and designed integrator and function is plotted, which is defined as = ‖ ( ) − h( )‖ to justify the validity of the designed digital integrator.