Building a generalized peres gate with multiple control signals

Abstract

We consider a physical realization of the generalized quantum Peres and Toffoli gates with n-control signals, implemented in a one-dimensional chain of nuclear spins (one half) in a strong magnetic field coupled by an Ising interaction. Quantum algorithms in such system can be performed by transverse electromagnetic radio-frequency field using a number of resonant π-pulses on the initial states. The maximum number of π-pulses needed for the implementation of the Peres gate with n-control signals is discussed. It is found, that required number of π-pulses linearly scales with the number n of the control signals of the generalized quantum Peres gate. Comparison of our studies with the known values of the quantum cost of the generalized Peres gate allows us to suggest that proposed physical implementation of the gate is more efficient. The fidelity parameter is used to study the performance of the generalized Peres gate as a function of the relative error of the resonance frequency. The limits of an imbalance of the generator settings remaining the gate well defined are determined.