Constantcost implementations of Clifford operations and multiply controlled gates using global interactions
Abstract
A frequent physicallevel requirement for the ability to implement quantum operations simultaneously is their commutativity. In this work, we asked if quantum computation by commuting Isingtype entangling operations and ``free'' singlequbit gates can be advantageous compared to quantum computation by the twoqubit gates and ``free'' singlequbit gates. We focused on the elements of the Clifford group and the multiply controlled gates. It turned out that such circuits and composite gates can be implemented with very little effort  using constantly or effectively constantly many blocks of commuting sets of gates, in all cases except some with the most severe restrictions on the number of ancillary qubits available. Specifically, we show constantcost implementations of Clifford operations with and without ancilla, constantcost implementation of the multiply controlled gates with linearly many ancillae, and an $O(\log^*(n))$ implementation of the $n$controlled singletarget gates using logarithmically many ancillae. This shows significant (asymptotic) improvement of circuits enabled by the global gates vs those over single and twoqubit gates.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 arXiv:
 arXiv:2207.08691
 Bibcode:
 2022arXiv220708691B
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity;
 Computer Science  Emerging Technologies