Non-Abelian braiding of graph vertices in a superconducting processor
Google Quantum AI and Collaborators, T. I. Andersen, Yuri D. Lensky, K. Kechedzhi, Ilya Drozdov, Andreas Bengtsson, Sabrina Hong, Alexis Morvan, Xiao Mi, Alex Opremcak, Rajeev Acharya, R. M. Allen, M. Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, L. Brill, M. Broughton, B. B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Z. Chen, Benjamin Chiaro, Desmond Chik, C. W. Chou, J. Cogan, Roberto Collins, P. Conner, W. Courtney, Alexander L. Crook, Ben Curtin, D. M. Debroy, Alexander Del Toro Barba, Sean Demura, A. Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, V. S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, A. G. Fowler, Brooks Foxen, William Giang, Craig Gidney, D. Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, M. C. Hamilton, M. Hansen, Matthew P. Harrigan, Sean D. Harrington, Paula Heu, Jeremy Hilton, M. R. Hoffmann, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, S. V. Isakov, Justin Iveland, E. Jeffrey, Jiang Zhang, C. Jones, Pavol Juhás, Dvir Kafri, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, P. V. Klimov, Andrey Klots, A. N. Korotkov, F. Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, K.-M. Lau, Lily Laws, J. Lee, Kenny Lee, Brian Lester, Alexander T. Lill, W. Liu, Aditya Locharla
Abstract
Abstract Indistinguishability of particles is a fundamental principle of quantum mechanics 1 . For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged 2,3 . However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions 4–8 . Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals 9–22 , the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons 9,10 , we implement a generalized stabilizer code and unitary protocol 23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.