Experimental Quantum Metrology Based On Nuclear Magnetic Resonance System

As a cross-discipline that combines quantum mechanics and statistical inference,quantum metrology has become one of the most important applications of quantum technology in the real world.It uses non-classical resources such as quantum entanglement,can exceed the precision limit defined by classical parameter estimation theory,and shows pivotal applications in frontier precision measurement fields such as gravitational wave detection,biological measurement,and magnetic field measurement.Although quantum metrology has been well investigated in theory,it’s challenging to show the quantum advantages in practical quantum systems,especially for large-scale quantum systems under noise.First of all,limited by the exponential growth of Hilbert space dimension and experimental control error of quantum systems,it is intractable to simulate the complex dynamics process of real quantum systems on classical computers and engineer the optimal quantum probe state.Besides,quantum systems inevitably couple to the environment,during which quantum coherence and entanglement can be destroyed,thus losing the encoded information.Finally,the application of the optimal measurement faces similar problems in engineering the optimal quantum probe state,and it becomes more complex to design the optimal readout scheme that can weigh the precision of each parameter when extending to multi-parameter estimation scenarios.To overcome or relieve the above problems in the process of quantum metrology and demonstrate quantum advantages,this thesis elaborates author’s experimental study of quantum metrology based on nuclear magnetic resonance system.It mainly includes the following contents:1.Aiming at the problem of engineering quantum probe state in large-scale quantum systems under noise,this thesis develops a method for extracting quantum Fisher information from quantum probe state with Loschmidt echo,and designs an optimal probe state engineering scheme based on the framework of variational quantum metrology.The ten-spin optimal quantum probe state is experimentally engineered by variational optimization and achieves a 12.4dB enhancement of the phase measurement precision over the standard quantum limit.Compared with current methods for extracting quantum Fisher information,this method requires fewer additional qubits and measurement time,thus being scalable.It provides a powerful tool for studying quantum entanglement in many-body systems and engineering the optimal quantum probe state in large-scale quantum systems.2.For the destruction of the encoded information in quantum systems caused by environmental decoherence,this thesis proposes a new approach for critical quantum metrology based on the first-order quantum phase transition.Not only is it robust against noise,but also it can relieve the problem of "critical slowing down"by tuning the energy gap at the critical point.Utilizing the means of adiabatic evolution,the Heisenberg scaling for measuring the magnetic field is experimentally achieved on the two-spin system.This experiment represents important progress in realizing quantum metrology using quantum critical systems.This scheme is promising to be realized in more quantum systems such as NV centers,cold atoms,and superconducting circuits.3.Aiming at the problem of designing readout schemes for quantum multiparameter estimation,this thesis investigates the specific problem of quantum state reconstruction and proposes an optimal scheme that requires minimal experimental measurements with the highest precision.This scheme makes an optimal tradeoff for the precision of each parameter in the quantum state to be reconstructed by optimizing the readout operations with a machine-learning algorithm.It’s applied to the reconstruction of 10-spin quantum states with star symmetry.The numerical results show its scalability and improvement in precision,thus assisting with the design of the optimal measurement for quantum state reconstruction.In general,starting from the challenges of realizing quantum-enhanced metrology in practical quantum systems,this thesis conducts experimental research and exploration of new approaches to quantum metrology.These investigations help improve the precision of parameter estimation under the limits of practical quantum devices,such as environmental noise,imperfect controls,measurement errors,and so on,thus approaching the optimal precision limit in the practical metrological task.