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%20excel%20on%20tasks%20using%20functional%20data%2C%20such%20as%20those%20originating%20from%20partial%20differential%20equations.%20Such%20characteristics%20render%20them%20an%20effective%20approach%20for%20simulating%20the%20time%20evolution%20of%20quantum%20wavefunctions%2C%20which%20is%20a%20computationally%20challenging%2C%20yet%20coveted%20task%20for%20understanding%20quantum%20systems.%20In%20this%20manuscript%2C%20we%20use%20FNOs%20to%20model%20the%20evolution%20of%20random%20quantum%20spin%20systems%2C%20so%20chosen%20due%20to%20their%20representative%20quantum%20dynamics%20and%20minimal%20symmetry.%20We%20explore%20two%20distinct%20FNO%20architectures%20and%20examine%20their%20performance%20for%20learning%20and%20predicting%20time%20evolution%20using%20both%20random%20and%20low-energy%20input%20states.%20Additionally%2C%20we%20apply%20FNOs%20to%20a%20compact%20set%20of%20Hamiltonian%20observables%20(%24simtext%7Bpoly%7D(n)%24)%20instead%20of%20the%20entire%20%242%5En%24%20quantum%20wavefunction%2C%20which%20greatly%20reduces%20the%20size%20of%20our%20inputs%20and%20outputs%20and%2C%20consequently%2C%20the%20requisite%20dimensions%20of%20the%20resulting%20FNOs.%20Moreover%2C%20this%20Hamiltonian%20observable-based%20method%20demonstrates%20that%20FNOs%20can%20effectively%20distill%20information%20from%20high-dimensional%20spaces%20into%20lower-dimensional%20spaces.%20The%20extrapolation%20of%20Hamiltonian%20observables%20to%20times%20later%20than%20those%20used%20in%20training%20is%20of%20particular%20interest%2C%20as%20this%20stands%20to%20fundamentally%20increase%20the%20simulatability%20of%20quantum%20systems%20past%20both%20the%20coherence%20times%20of%20contemporary%20quantum%20architectures%20and%20the%20circuit-depths%20of%20tractable%20tensor%20networks.)
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