Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
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Abstract
High-fidelity generation of two-qubit gates is important for quantum computation, since such gates are components of popular universal sets of gates. Here, we consider the problem of high-fidelity generation of two-qubit C-NOT and C-PHASE (with a detailed study of C–Z) gates in presence of the environment. We consider the general situation when qubits are manipulated by coherent and incoherent controls; the latter is used to induce generally time-dependent decoherence rates. For estimating efficiency of optimization methods for high-fidelity generation of these gates, we study quantum control landscapes which describe the behavior of the fidelity as a function of the controls. For this, we generate and analyze the statistical distributions of best objective values obtained by incoherent GRadient Ascent Pulse Engineering (inGRAPE) approach. We also apply inGRAPE and a dual annealing algorithm (DAA) based on a stochastic zeroth-order method to numerically estimate minimal infidelity values. The results are different from the case of single-qubit gates and indicate a smooth trap-free behavior of the fidelity.