Efficient realization of quantum-enhanced metrological advantages with Loschmidt echo

Quantum metrology leverages quantum resources such as quantum entanglement or squeezing in many-body systems to achieve precision beyond the limits of classical measurement schemes, offering significant implications for both fundamental science and advanced technologies. However, in practical many-body quantum systems under noise, demonstrating the advantages of quantum resources for metrology has faced numerous challenges. On one hand, as the size of quantum systems increases, the classical resources required for their simulation and characterization grow exponentially, leading to the so-called “exponential disaster.” This makes it difficult to design the optimal control strategies in advance using purely classical optimization methods to efficiently prepare quantum probes with high sensitivity. On the other hand, practical quantum probes usually deviate from theoretical expectations due to imperfections such as control errors, readout errors, and environmental decoherence, thus reducing the measurement precision.

Variational quantum precision measurement provides a new paradigm for high-precision measurement by adopting a classical-quantum hybrid framework, which leverages the dynamical evolution of the quantum system itself, and dynamically adjusting system control parameters with classical optimization algorithms. It offers an effective solution to the aforementioned scientific issues. However, efficiently evaluating the performance of quantum probes in many-body quantum systems remains a core challenge in the field, as it largely determines the efficiency of precision improvement and ultimate performance of quantum precision measurement.

Recently, Professor Peng Xinhua from the CAS Key Laboratory of Microscale Magnetic Resonance at the University of Science and Technology of China, and Professor Yuan Haidong from the Chinese University of Hong Kong, collaborated on a systematic study of variational quantum metrology based on Loschmidt echo. The study introduced a scalable and efficient approach to evaluate quantum probes by measuring Loschmidt echo and further validated this method experimentally on a nuclear magnetic resonance quantum processor. The results indicate that, through variational quantum optimization, the theoretical precision limit of the experimentally prepared quantum probes can be significantly improved, demonstrating a precision gain of 12.4 dB over uncorrelated quantum states in phase estimation applications. This work is expected to provide new insights into the application of noisy many-body quantum systems in quantum metrology during the NISQ era. The results have been published in National Science Review (2025, Issue xx) under the title “Variational Quantum Metrology with Loschmidt Echo,”, with Professors Xinhua Peng and Haidong Yuan as co-corresponding authors.

The research team developed a theoretical method for characterizing and evaluating quantum probes based on Loschmidt echo and designed a scalable metrology scheme. The performance of a quantum probe for precision measurement is typically characterized by quantum Fisher information (QFI). However, it is challenging to directly and effectively measure QFI in experiments. Existing methods often require measurement resources that grow exponentially with system size or introduce additional physical qubits, which significantly limits the practical application of variational quantum metrology. The research team, leveraging the connection between Loschmidt echo and QFI, along with hardware-efficient variational quantum circuit design, proposed a universal and scalable quantum Fisher information extraction scheme in noisy environments. Compared to previous methods, this scheme requires only measurement resources that grow linearly with system size, providing the necessary conditions for the efficient characterization and evaluation of quantum probes. Furthermore, the research team conducted experimental demonstration on a nuclear magnetic resonance quantum processor, realizing the preparation and optimization of a 10-spin high-sensitivity quantum probe. In the experiment, based on the classical-quantum hybrid optimization framework of variational quantum metrology, the team evaluated the performance of the 10-spin quantum probe prepared by variational quantum circuits under practical noise by measuring Loschmidt echo. Additionally, they applied classical machine learning algorithms to iteratively optimize the parameters of the variational quantum circuits in the experiment, ultimately obtaining the optimal quantum probe state close to the theoretical expectation of the quantum Cramér-Rao bound. The research team also applied the optimized quantum probe to a phase estimation task, using a time-reversal-based readout method. This enabled a simple and feasible phase estimation task that approaches the theoretical precision limit. They achieved a precision gain of 12.4 dB compared to uncorrelated quantum states, fully demonstrating the quantum-enhanced metrological advantages brought by many-body effects.