## Simulating quantum circuits by classical circuits

23 Jul 2019  ·  Wang Daochen ·

In a recent breakthrough, Bravyi, Gosset and K\"{o}nig (BGK) [Science, 2018] proved that "simulating" constant depth quantum circuits takes classical circuits $\Omega(\log n)$ depth. In our paper, we first formalise their notion of simulation, which we call "possibilistic simulation"... Then, from well-known results, we deduce that their circuits can be simulated in depth $O(\log^{2} n)$. Separately, we construct explicit classical circuits that can simulate any depth-$d$ quantum circuit with Clifford and $t$ $T$-gates in depth $O(d+t)$. Our classical circuits use $\{\text{NOT, AND, OR}\}$ gates of fan-in $\leq 2$. read more

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Quantum Physics