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0.5x A Presses / But First We Need to Talk About Parallel Universes - QPU - Formal version
![A formal definition of QPU-alignment To begin, consider product of half-open intervals-L,L]n-Rn where L < 32768, Let f :-L,L]n-1 → R be a piecewise continuous, linear function. We note that graph of f , denoted「(f) , can be thought of as a (n-1)-dimensional manifold composed of simplices (i.e. (n - 1)-dimensional analogues of triangles) and that VF is well-defined and constant in the interior of each simplex. Extend f to a function f -32768, 32768]1R by setting f (x) if x E-L, L]- 0 otherwise Endow「( f ) with the usual subspace topology inherited from Rn) then identify boundary points (... ,-32768 space as the torus「(f) / ~ with the quotient topology. We are now ready for a formal definition of QPU-alignment ) ~(...,32768,...). We then define the PU Definition 1 Let r : [0,S] →「(f) / ~ be a piecewise diferentiable path parametrized by arclength. We sav r is QPU-aligned if 4-65536 Ir' (s) max())1 for all s in the domain of r such that r' (s) exists Note that we often consider the case in which the last coordinate of r(i.e the usual Euclidean inner product r' (s) (0,...0, 1)) is constrained to have magnitude γ (S). 2 where n is a non-negative integer and A is some constant that is dependent only In the special case in which n is further constrained to be even, we call on such r a Henry path](https://i.kym-cdn.com/photos/images/original/001/067/875/082.png)
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