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We analyze the multifractality of the fidelity in an engineered Toffoli gate.Using quantum control methods, we define several optimization problems whoseglobal solutions realize the gate in a chain of three qubits with XY Heisenberginteraction. We perturb the system by introducing imperfections in the form of$1/f$ noise to the interqubit couplings. Multifractal analysis shows that thedegree of multifractality in the gate fidelity increases when optimized controlpulses used to render the fidelity are less sensitive to variations in theinterqubits coupling strengths.

Multifractality in the fidelity of the Toffoli gate