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+excel+on+tasks+using+functional+data%252C+such+as+those+originating+from+partial+differential+equations.+Such+characteristics+render+them+an+effective+approach+for+simulating+the+time+evolution+of+quantum+wavefunctions%252C+which+is+a+computationally+challenging%252C+yet+coveted+task+for+understanding+quantum+systems.+In+this+manuscript%252C+we+use+FNOs+to+model+the+evolution+of+random+quantum+spin+systems%252C+so+chosen+due+to+their+representative+quantum+dynamics+and+minimal+symmetry.+We+explore+two+distinct+FNO+architectures+and+examine+their+performance+for+learning+and+predicting+time+evolution+using+both+random+and+low-energy+input+states.+Additionally%252C+we+apply+FNOs+to+a+compact+set+of+Hamiltonian+observables+(%2524simtext%7bpoly%7d(n)%2524)+instead+of+the+entire+%25242%5en%2524+quantum+wavefunction%252C+which+greatly+reduces+the+size+of+our+inputs+and+outputs+and%252C+consequently%252C+the+requisite+dimensions+of+the+resulting+FNOs.+Moreover%252C+this+Hamiltonian+observable-based+method+demonstrates+that+FNOs+can+effectively+distill+information+from+high-dimensional+spaces+into+lower-dimensional+spaces.+The+extrapolation+of+Hamiltonian+observables+to+times+later+than+those+used+in+training+is+of+particular+interest%252C+as+this+stands+to+fundamentally+increase+the+simulatability+of+quantum+systems+past+both+the+coherence+times+of+contemporary+quantum+architectures+and+the+circuit-depths+of+tractable+tensor+networks.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.52c67366d2f7b795ee5e3f92f8d1f657%3frik%3dbc3J5OKgjdWBzg%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Neural+Operator+Learning+Appliation+Visualized&FORM=IRPRST&ck=A6089442ECD25CEC76924D62E9A40C28&selectedIndex=33&itb=0)
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