Robust control of a not gate by composite pulses

Abstract

We present a general procedure to implement a NOT gate by composite pulses robust against both offset uncertainties and control field variations. We define different degrees of robustness in this two-parameter space, namely along one, two or all directions. We show that the phases of the composite pulse satisfy a nonlinear system, and can be computed analytically or numerically.

Composite pulses for high fidelity population transfer in three-level systems

“…On the other hand, as shown in Refs. [23][24][25][26], the fidelity improves with the increase in the number of pulses. However, considering the finite coherence time, a large number of pulses would cost long evolution time, which is tremendously detrimental for quantum computation.…”

“…The CPs technique, comprised of a well-organized train of constant pulses with determined pulse areas and relative phases, was conceived in early nuclear magnetic resonance (NMR) [18][19][20][21]. To date, this technique has been used extensively in QIP [22][23][24][25][26][27][28][29][30][31]. One unique feature of CPs is that the pulse sequence is available to compensate for the systematic error in any physical parameters (e.g., pulse duration, pulse amplitude, detuning, Stark shift, etc.)…”

Robust population inversion in three-level systems by composite pulses

“…CPs technique was born in the field of nuclear magnetic resonance [50][51][52][53][54]. Over the past decade, CPs have provided a number of solutions in quantum computation [55][56][57][58][59][60][61][62][63][64], due to their extremely high accuracy, robust manner against errors, and extraordinary flexibility [65]. Generally speaking, CPs is composed of a series precise constant pulses with different relative phases.…”

“…Recently, PMCPs have been designed to produce a rotation at a predefined angle in the Bloch sphere [57,66], where the errors resulting from the pulse area could be gradually compensated with the increase of the pulse number. In addition, PMCPs could also be applied in the robust implementation of quantum NOT gate [63], where the design process is based on the solutions of a set of trigonometric equations. Furthermore, the quantum NOT gate could be robust against both offset uncertainties and control field variations by a very small number of modulation parameters.…”

“…SMCPs are used to implement dynamically corrected single-qubit gates on singlet-triplet qubits [68], where the qubit manipulations are handled by adjusting the electrically controlled exchange coupling strength. Note that most works [55][56][57][58][59][60][61][62][63][64][65][66][67][68] of CPs are based on twolevel systems. Recently, the CPs have been extended to the three-level systems and provided many creative works [69][70][71][72][73][74], such as the implementation of high-fidelity composite quantum gates [69,70] and efficient detection of chiral molecules [71].…”