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Pythagorean Coupling in a Four-Level Josephson Phase Qudit


  Elisha Svetitsky [1]  ,  Haim Suchowski [2,3]  ,  Roy Resh [1]  ,  Yoni Shalibo [1]  ,  Nadav Katz [1]  
 [1] Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
[2] Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
[3] NSF Nanoscale Science and Engineering Center, 3112 Etcheverry Hall, University of California, Berkeley, California 94720, USA

Multi-level qudits are advantageous for a number of applications of quantum information science, but introduce complex dynamics which must be understood and controlled. The recently proposed theory of Pythagorean coupling uses the well-known isomorphism between the SO(4) group and SU(2)xSU(2) product group to map the dynamics of a four-level system onto two uncoupled Bloch spheres, uncovering a method of transferring population between non-adjacent qudit states with a single continuous excitation. We demonstrate the first experimental implementation of this coupling scheme on a superconducting Josephson phase qudit and observe a crossover from SO(4) to SU(4) dynamics.