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

TL;DR

This paper demonstrates that quantum circuits using global Ising-type entangling gates can implement a broad class of unitary operations, including Clifford and multiply controlled gates, with constant or near-constant cost, offering significant efficiency advantages.

Contribution

It introduces methods for constant-cost implementation of Clifford and multiply controlled gates using global interactions, improving quantum circuit efficiency.

Findings

Constant-cost Clifford gate implementation with and without ancillae.

Linear-cost multiply controlled gates with linearly many ancillae.

Logarithmic-depth implementation of n-controlled gates with logarithmic ancillae.

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 $O(\log^*(n))$ 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.