Constant-cost implementations of Clifford operations and multiply controlled gates using global interactions

Abstract

We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type 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 constant-cost implementations of Clifford operations with and without ancillae, constant-cost implementation of the multiply controlled gates with linearly many ancillae, and an $O({\log }^{\ast }(n))$ cost implementation of the $n$-controlled single-target gates using logarithmically many ancillae. This shows a significant asymptotic advantage of circuits enabled by the global entangling gates.

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• Constant-depth circuits for Boolean functions and quantum memory devices using multi-qubit gates
• Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds
• Multi-Mode Global Driving of Trapped Ions for Quantum Circuit Synthesis
• Pulse optimization for high-precision motional-mode characterization in trapped-ion quantum computers
• Engineering long-range and multi-body interactions via global kinetic constraints