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I have to test a simulator with a high number of random stabilizer circuits. One way to create random stabilizer circuits is to generate random graph states and convert those to circuits, this, however, will always yield optimized circuits (in particular the entanglement gates will be optimized).

Is there a systematical way to generate randomized unoptimized stabilizer circuits? Can this algorithm take the starting state into account i.e. if the simulation will always start from $$|+\rangle = \left(\bigotimes\limits_{i=0}^{n-1} H_i \right)|0\rangle \ ?$$

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  • $\begingroup$ Do you just want random strings in the letters of allowed gates of length $k$? Or maybe $k$ is random too? Just randomly the next gate independently of all the others? $\endgroup$
    – AHusain
    Nov 16, 2019 at 20:50
  • $\begingroup$ @AHusain The problem with generating random strings of gates is that many clifford gates are closely related, meaning that some classes of stabilizer codes would have a way higher probability than others. But maybe I will have to resort to that solution. $\endgroup$ Nov 17, 2019 at 9:56
  • $\begingroup$ Maybe if you say precisely what probability measure you want first. $\endgroup$
    – AHusain
    Nov 19, 2019 at 8:18

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