ConstantCost Implementations of Clifford Operations and MultiplyControlled Gates Using Global Interactions
Abstract
We consider quantum circuits composed of singlequbit operations and global entangling gates generated by Isingtype Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum algorithms at a very low cost—using a constant or effectively constant number of global entangling gates. Specifically, we report constantcost implementations of Clifford operations with and without ancillae, constantcost implementation of the multiplycontrolled gates with linearly many ancillae, and an O (log^{*}(n )) cost implementation of the n controlled singletarget gates using logarithmically many ancillae. This shows a significant asymptotic advantage of circuits enabled by the global entangling gates.
 Publication:

Physical Review Letters
 Pub Date:
 December 2022
 DOI:
 10.1103/PhysRevLett.129.230501
 arXiv:
 arXiv:2207.08691
 Bibcode:
 2022PhRvL.129w0501B
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity;
 Computer Science  Emerging Technologies
 EPrint:
 Phys. Rev. Lett. 129, 230501 (2022)