Nuclear magne­tic resonance spectro­scopy (NMR spectroscopy)

Nuclear Magne­tic Reson­nace (NMR)  spectro­scopy is funda­men­tally a time-domain experi­ment: you perturb a spin system with a pulse,  whatch the magne­tiza­tion evolve under the spin Hamil­to­nian, and  observe Fourier trans­form the resul­ting signal to extract the spectrum. This makes it a natural appli­ca­tion of quantum simula­tion of dynamics rather than quantum algorithms aimed at ground-state prepa­ra­tion. On a quantum compu­ter, the time evolu­tion opera­tor can, for example, be imple­men­ted via Trotte­riza­tion, while the magne­tiza­tion is read out as expec­ta­tion values of spin opera­tors at succes­sive time steps. Classi­cally, the same dynamics can be propa­ga­ted using Neural Quantum States (NQS) in combi­na­tion with Time-Depen­dent Varia­tio­nal Monte Carlo (TD-VMC).  The Quantum Complex Exponen­tial Least Squares (QCELS) is parti­cu­larly attrac­tive in this context because it naturally genera­tes a time-series signal that NMR analy­sis already relies on, and can extract multi­ple spectral frequen­cies simul­ta­neously with far fewer circuit evalua­tions than a full Trotte­ri­zed simulation.