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

• URL: http://arxiv.org/abs/2207.08691v2
• Date: Thu, 1 Dec 2022 17:21:23 GMT
• Title: Constant-cost implementations of Clifford operations and multiply controlled gates using global interactions
• Authors: Sergey Bravyi, Dmitri Maslov, and Yunseong Nam
• Abstract summary: 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 at a very low cost -- using a constant or effectively constant number of global entangling gates.
• Score: 7.165608198928042
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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