Quantum-Enhanced Parameter Estimation in Multilevel Systems: Experimental Verification in a Superconducting Qutrit Sensor

As a cornerstone of advanced quantum techniques, parameter estimation is fundamental to precision measurement in physics. Although quantum-enhanced estimation of single parameter has been demonstrated in various two-level systems, measurable parameters remain highly limited. While multilevel quantum systems are capable of measuring diverse parameters, achieving this under general quantum dynamics remains a daunting challenge. Here, we propose a versatile framework for parameter estimation in multilevel systems under general quantum dynamics. Furthermore, we experimentally demonstrate quantum-enhanced measurement of relative values between multiple parameters using a superconducting qutrit sensor. In our experiments, two resonant microwave drives with distinct phases and amplitudes are used to coherently encode parameters into the qutrit. We achieve quantum-enhanced measurement of the ratio of two Rabi frequencies, the phase sum, and the phase difference between the microwave fields, demonstrating precision approaching the Heisenberg limit. Our Letter advances the frontier of quantum metrology and offers new possibilities for high-precision, resource-efficient measurements, with broad applications across science and technology.