A noise-spectrum analysis without spurious harmonics is developed and applied to a molecular qubit, which has complicated composition of spin bath. A type of molecular-qubit transition-metal complex $({\mathrm{PPh}}_4{)}_2[{\mathrm{Cu(mnt)}}_2]$ is utilized to demonstrate our method. Various types of nuclear spins in its spin bath, such as ${}^1\mathrm{H}$, ${}^{31}\mathrm{P}$, ${}^{13}\mathrm{C}$, and ${}^{63}\mathrm{Cu}$ are resolved with our method, while only the signal from ${}^1\mathrm{H}$ can be resolved by traditional noise-spectrum analysis. Our result provides a noise-spectrum analysis without spurious harmonics, which enables the design of optimal quantum-control methods, improves the material engineering, and generally enhances coherence for molecular qubits.

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• Open quantum systems & decoherence
• Quantum control
• Quantum information with solid state qubits
• Quantum protocols
• Zeeman effect
• Molecules
• Electron spin resonance
• Nuclear magnetic resonance