might be that Nature needs to expend more computational effort to calculate a particle’s entire trajectory than to calculate its position at any individual time.  The reason is that the former requires keeping track of multiple-time correlations.  And indeed, I showed in [@aar:qchv] that under any hidden-variable theory satisfying a reasonable axiom called indifference to the identity, the ability to sample the hidden variable’s history would let us solve the Graph Isomorphism problem in polynomial time.  For intuitively, given two graphs $G$ and $H$ with no nontrivial automorphisms, one can easily prepare a uniform superposition over all permutations of $G$ and $H$:$$\frac{1}{\sqrt{2n!}}\sum_{\sigma\in S_{n}}\left(  \left\vert 0\right\rangle
\left\vert \sigma\right\rangle \left\vert \sigma\left(  G\right)
\right\rangle +\left\vert 1\right\rangle \left\vert \sigma\right\rangle
\left\vert \sigma\left(  H\right)  \right\rangle \right)  .$$ Then measuring the third register yields a state of the form $\left\vert
i\right\rangle \left\vert \sigma\right\rangle $ if $G$ and $H$ are not isomorphic, or $\left(  \left\vert 0\right\rangle \left\vert \sigma
\right\rangle +\left\vert 1\right\rangle \left\vert \tau\right\rangle \right)
/\sqrt{2}$ for some $\sigma\neq\tau$ if they are isomorphic.  Unfortunately, if then we measured this state in the standard basis, we would get no information whatsoever, and work of myself [@aar:col], Shi [@shi], and Midrijanis [@midrijanis] shows that no black-box quantum algorithm can do much 