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Better MCX Decomposition with logarithmic Toffoli Depth #13913

@patelvyom

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@patelvyom

Rise of conditionally clean ancillae for optimizing quantum circuits provides an algorithm to decompose MCX with n-controls into

  • 2n − 3 Toffoli and O(n) depth using 1 clean ancilla
  • 2n − 3 Toffoli and O(log(n)) depth using 2 clean ancilla
  • 4n − 8 Toffoli and O(n) depth using 1 dirty ancilla
  • 4n - 8 Toffoli and O(log(n)) depth using 2 dirty ancilla

I already have a working implementation and want to add a pull request. However, I don't know where the implementation should go. I was thinking qiskit/synthesis/multi_controlled/mcx_synthesis.py.

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