Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving

TL;DR

This paper investigates optimizing high-fidelity two-qubit gates, specifically C-NOT and C-PHASE, using quantum control landscapes and incoherent control methods to understand their efficiency and landscape topology.

Contribution

It introduces a comprehensive analysis of quantum control landscapes for two-qubit gates with environmental effects, demonstrating smooth, trap-free behavior in fidelity optimization.

Findings

Fidelity landscapes are smooth and trap-free for two-qubit gates.

Incoherent control can effectively optimize gate fidelity.

Statistical analysis of optimization results shows consistent high performance.

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 behaviour 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 stochastic zero-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 behaviour of the fidelity.