Nuclear Magnetic Resonance (NMR) plays a central role in developing quantum information sciences and technologies. Key features such as its non-invasive nature and the ability to process information on nuclear spins by versatile quantum control designs with electromagnetic fields, have made NMR to become a powerful technique for sensing systems from atomic and molecular scales with spectroscopy to millimeters in imaging. This brief overview provides quantum sensing tools with which we are contributing from Latin America, by combining quantum dynamical control and estimation strategies with NMR methods to probe physical, chemical, and biological processes. It introduces the basic and key concepts on how controlled spin-sensors can monitor the correlation dynamics of their environment, and selectively and optimally infer its relevant parameters. Then these concepts are illustrated with state-of-the-art implementations for characterizing (i) biological tissue microstructure with diffusion weighting imaging, (ii) quantum information dynamics and scrambling in out-of-equilibrium systems with solid-state NMR quantum simulations, and (iii) molecular structures by selective estimation of spin–spin couplings and online learning control designs with experimental proposals. We expect these concepts will motivate the development of quantum dynamical control of spin sensors to monitor systems in a variety of fields, and in particular to exploit the non-invasive strength of NMR, e.g. in biomedical diagnosis. • Quantum control and estimation tools probe physical, chemical, biological processes. • Efficient quantum sensing for maximizing relevant environmental information. • Biological tissue microstructure characterization with diffusion weighting imaging. • Assessing fragility of quantum information dynamics in out-of-equilibrium systems. • Selective estimation of spin–spin couplings and online learning control designs.
We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component
ght and related geometric observables, where
h is a controllable post-quench Hamiltonian parameter and
t is real time. The framework treats
h and
t as coordinates of an extended information manifold
(h,t). The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.
Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number
K of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.