# A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits

@article{Amy2013AMA, title={A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits}, author={Matthew Amy and Dmitrii L. Maslov and Michele Mosca and Martin Roetteler}, journal={IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, year={2013}, volume={32}, pages={818-830} }

We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute force algorithms. As an illustration of our method, we implemented this algorithm and found factorizations of commonly used quantum logical operations into elementary gates in the Clifford+T set. In particular, we report a decomposition of the Toffoli gate over the set of Clifford and T gates. Our decomposition…

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