Using Stim, is there an efficient way to evaluate a particular amplitude, i.e. $\langle 0|U|0\rangle$ (including the phase), where U is a circuit of Clifford gates?
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Stim has no built-in way to track this information. The Tableau class doesn't have a place to store global phase information, and the TableauSimulator class doesn't try to track the global phase.
It's possible you could use Stim's classes to deal with some of the boilerplate of implementing phase tracking, but Stim itself does not do it.
Craig Gidney
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