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However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>i<\/mml:mi><mml:mi>m<\/mml:mi><mml:mi>p<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>s<\/mml:mi><mml:mi>s<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>b<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>e<\/mml:mi><\/mml:math>. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">Hamiltonian amplification<\/mml:mtext><\/mml:mrow><\/mml:math> (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.<\/jats:p>","DOI":"10.22331\/q-2020-05-25-271","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T14:55:31Z","timestamp":1590418531000},"page":"271","source":"Crossref","is-referenced-by-count":18,"title":["Amplification of quadratic Hamiltonians"],"prefix":"10.22331","volume":"4","author":[{"given":"Christian","family":"Arenz","sequence":"first","affiliation":[{"name":"Frick Laboratory, Princeton University, Princeton NJ 08544, United States"}]},{"given":"Denys I.","family":"Bondar","sequence":"additional","affiliation":[{"name":"Tulane University, New Orleans, LA 70118, United States"}]},{"given":"Daniel","family":"Burgarth","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia"}]},{"given":"Cecilia","family":"Cormick","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica Enrique Gaviola, CONICET and Universidad Nacional de C\u00f3rdoba, Ciudad Universitaria, X5016LAE, C\u00f3rdoba, Argentina"}]},{"given":"Herschel","family":"Rabitz","sequence":"additional","affiliation":[{"name":"Frick Laboratory, Princeton University, Princeton NJ 08544, United States"}]}],"member":"9598","published-online":{"date-parts":[[2020,5,25]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"L. Dicarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature, 467(7315):574\u2013578, Sep 2010. doi:10.1038\/nature09416.","DOI":"10.1038\/nature09416"},{"key":"1","doi-asserted-by":"publisher","unstructured":"T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert. Entangling mechanical motion with microwave fields. Science, 342(6159):710\u2013713, Nov 2013. doi:10.1126\/science.1244563.","DOI":"10.1126\/science.1244563"},{"key":"2","doi-asserted-by":"publisher","unstructured":"D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovi\u0107, C. Langer, T. Rosenband, and D. J. Wineland . Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature, 422(6930):412\u2013415, Mar 2003. doi:10.1038\/nature01492.","DOI":"10.1038\/nature01492"},{"key":"3","doi-asserted-by":"publisher","unstructured":"T. R. Tan, J. P. Gaebler, Y. Lin, Y. Wan, R. Bowler, D. Leibfried, and D. J. Wineland. Multi-element logic gates for trapped-ion qubits. Nature, 528(7582):380\u2013383, Dec 2015. doi:10.1038\/nature16186.","DOI":"10.1038\/nature16186"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Thaddeus D Ladd, Fedor Jelezko, Raymond Laflamme, Yasunobu Nakamura, Christopher Monroe, and Jeremy Lloyd O\u2019Brien. Quantum computers. Nature, 464(7285):45\u201353, Mar 2010. doi:10.1038\/nature08812.","DOI":"10.1038\/nature08812"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Advances in quantum metrology. 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Quantum Information Processing, 15(10), Nov.","DOI":"10.1007\/s11128-016-1405-x"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Lorenza Viola, Emanuel Knill, and Seth Lloyd. Dynamical decoupling of open quantum systems. Phys. Rev. Lett., 82:2417\u20132421, Mar 1999. doi:10.1103\/PhysRevLett.82.2417.","DOI":"10.1103\/PhysRevLett.82.2417"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Christian Arenz, Daniel Burgarth, and Robin Hillier. Dynamical decoupling and homogenization of continuous variable systems. Journal of Physics A: Mathematical and Theoretical, 50(13):135303, Mar 2017. doi:10.1088\/1751-8121\/aa6017.","DOI":"10.1088\/1751-8121\/aa6017"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Daniel Lidar and Brun Todd. Quantum error correction, Sep 2013. doi:10.1017\/CBO9781139034807.","DOI":"10.1017\/CBO9781139034807"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Daniel A. Lidar, Paolo Zanardi, and Kaveh Khodjasteh. 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Quantum Science and Technology, 3(2):025001, Jan 2018. doi:10.1088\/2058-9565\/aa9d15.","DOI":"10.1088\/2058-9565\/aa9d15"},{"key":"35","doi-asserted-by":"publisher","unstructured":"K. Lake, S. Weidt, J. Randall, E. D. Standing, S. C. Webster, and W. K. Hensinger. Generation of spin-motion entanglement in a trapped ion using long-wavelength radiation. Phys. Rev. A, 91:012319, Jan 2015. doi:10.1103\/PhysRevA.91.012319.","DOI":"10.1103\/PhysRevA.91.012319"},{"key":"36","doi-asserted-by":"publisher","unstructured":"J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett., 78:3221\u20133224, Apr 1997. doi:10.1103\/PhysRevLett.78.3221.","DOI":"10.1103\/PhysRevLett.78.3221"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Christian Arenz and Herschel Rabitz. Controlling qubit networks in polynomial time. Phys. Rev. Lett., 120:220503, May 2018. doi:10.1103\/PhysRevLett.120.220503.","DOI":"10.1103\/PhysRevLett.120.220503"},{"key":"38","doi-asserted-by":"publisher","unstructured":"S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock. Quantum amplification of mechanical oscillator motion. Science, 364(6446):1163\u20131165, 2019. doi:10.1126\/science.aaw2884.","DOI":"10.1126\/science.aaw2884"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Lorenza Viola and Emanuel Knill. Robust dynamical decoupling of quantum systems with bounded controls. Phys. Rev. Lett., 90:037901, Jan 2003. doi:10.1103\/PhysRevLett.90.037901.","DOI":"10.1103\/PhysRevLett.90.037901"},{"key":"40","doi-asserted-by":"publisher","unstructured":"K. Khodjasteh and D. A. Lidar. Fault-tolerant quantum dynamical decoupling. Phys. Rev. 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