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arXiv · 2207.08691

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

Sergey Bravyi·Dmitri Maslov·Yunseong Nam
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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.

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Sergey Bravyi, Dmitri Maslov, Yunseong Nam. 2022-07-18. Constant-cost implementations of Clifford operations and multiply controlled gates using global interactions. https://doi.org/10.1103/physrevlett.129.230501

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