Multifractality in the fidelity of the Toffoli gate

TL;DR

This paper investigates how the multifractality of the fidelity in an engineered Toffoli gate is affected by control optimization and noise, revealing that less sensitive control pulses increase multifractality.

Contribution

It introduces a multifractal analysis of gate fidelity in a three-qubit system and links control robustness to multifractality under noise.

Findings

Multifractality in fidelity increases with control robustness.

Optimized control pulses reduce sensitivity to coupling variations.

Multifractal analysis provides insights into quantum gate stability.

Abstract

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