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The only requirement on the flexibility of the interaction is that it can be switched on and off for individual qubits. Our method yields a time-optimal implementation of the multi-qubit gates. We numerically demonstrate that the total multi-qubit gate time scales approximately linear in the number of qubits. Using this gate synthesis as a subroutine, we provide compilation strategies for important use cases: (i) we show that any Clifford circuit on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math> qubits can be implemented using at most <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><mml:mi>n<\/mml:mi><\/mml:math> multi-qubit gates without requiring ancilla qubits, (ii) we decompose the quantum Fourier transform in a similar fashion, (iii) we compile a simulation of molecular dynamics, and (iv) we propose a method for the compilation of diagonal unitaries with time-optimal multi-qubit gates, as a step towards general unitaries. As motivation, we provide a detailed discussion on a microwave controlled ion trap architecture with magnetic gradient induced coupling (MAGIC) for the generation of the Ising-type interactions.<\/jats:p>","DOI":"10.22331\/q-2023-04-20-984","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T12:27:51Z","timestamp":1681993671000},"page":"984","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":27,"title":["Synthesis of and compilation with time-optimal multi-qubit gates"],"prefix":"10.22331","volume":"7","author":[{"given":"Pascal","family":"Ba\u00dfler","sequence":"first","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Zipper","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher","family":"Cedzich","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Heinrich","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick H.","family":"Huber","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science and Technology, University of Siegen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Johanning","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science and Technology, University of Siegen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Kliesch","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Germany"},{"name":"Institute for Quantum and Quantum Inspired Computing, Hamburg University of Technology, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,4,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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