Baßler, PascalPascalBaßlerHeinrich, MarkusMarkusHeinrichKliesch, MartinMartinKliesch2024-04-122024-04-122024-03-13Quantum 8: 1279 (2024)https://hdl.handle.net/11420/46440Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates (GZZ gates). In this work, we first show that the synthesis of such quantum gates that are time-optimal is NP-hard. Second, we provide explicit constructions of special time-optimal multi-qubit gates. They have constant gate times and can be implemented with linearly many X-gate layers. Third, we develop a heuristic algorithm with polynomial runtime for synthesizing fast multi-qubit gates. Fourth, we derive lower and upper bounds on the optimal GZZ gate-time. Based on explicit constructions of GZZ gates and numerical studies, we conjecture that any GZZ gate can be executed in a time O(n) for n qubits. Our heuristic synthesis algorithm leads to GZZ gate-times with a similar scaling, which is optimal in this sense. We expect that our efficient synthesis of fast multi-qubit gates allows for faster and, hence, also more error-robust execution of quantum algorithms.en2521-327X20241279https://creativecommons.org/licenses/by/4.0/multi-qubit gates quantum computingComputer SciencesJournal Article10.15480/882.955110.22331/q-2024-03-13-127910.15480/882.95512307.11160Journal Article