Non-Abelian braiding of graph vertices in a superconducting processor
Abstract
Indistinguishability of particles is a fundamental principle of quantum mechanics. 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. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. 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, 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. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol 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 employing the anyons for quantum computation and utilize 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 toward fault-tolerant quantum computing.
Keywords
Cite
@article{arxiv.2210.10255,
title = {Non-Abelian braiding of graph vertices in a superconducting processor},
author = {Trond I. Andersen and Yuri D. Lensky and Kostyantyn Kechedzhi and Ilya Drozdov and Andreas Bengtsson and Sabrina Hong and Alexis Morvan and Xiao Mi and Alex Opremcak and Rajeev Acharya and Richard Allen and Markus Ansmann and Frank Arute and Kunal Arya and Abraham Asfaw and Juan Atalaya and Ryan Babbush and Dave Bacon and Joseph C. Bardin and Gina Bortoli and Alexandre Bourassa and Jenna Bovaird and Leon Brill and Michael Broughton and Bob B. Buckley and David A. Buell and Tim Burger and Brian Burkett and Nicholas Bushnell and Zijun Chen and Ben Chiaro and Desmond Chik and Charina Chou and Josh Cogan and Roberto Collins and Paul Conner and William Courtney and Alexander L. Crook and Ben Curtin and Dripto M. Debroy and Alexander Del Toro Barba and Sean Demura and Andrew Dunsworth and Daniel Eppens and Catherine Erickson and Lara Faoro and Edward Farhi and Reza Fatemi and Vinicius S. Ferreira and Leslie Flores Burgos and Ebrahim Forati and Austin G. Fowler and Brooks Foxen and William Giang and Craig Gidney and Dar Gilboa and Marissa Giustina and Raja Gosula and Alejandro Grajales Dau and Jonathan A. Gross and Steve Habegger and Michael C. Hamilton and Monica Hansen and Matthew P. Harrigan and Sean D. Harrington and Paula Heu and Jeremy Hilton and Markus R. Hoffmann and Trent Huang and Ashley Huff and William J. Huggins and Lev B. Ioffe and Sergei V. Isakov and Justin Iveland and Evan Jeffrey and Zhang Jiang and Cody Jones and Pavol Juhas and Dvir Kafri and Tanuj Khattar and Mostafa Khezri and Mária Kieferová and Seon Kim and Alexei Kitaev and Paul V. Klimov and Andrey R. Klots and Alexander N. Korotkov and Fedor Kostritsa and John Mark Kreikebaum and David Landhuis and Pavel Laptev and Kim-Ming Lau and Lily Laws and Joonho Lee and Kenny Lee and Brian J. Lester and Alexander Lill and Wayne Liu and Aditya Locharla and Erik Lucero and Fionn D. Malone and Orion Martin and Jarrod R. McClean and Trevor McCourt and Matt McEwen and Kevin C. Miao and Amanda Mieszala and Masoud Mohseni and Shirin Montazeri and Emily Mount and Ramis Movassagh and Wojciech Mruczkiewicz and Ofer Naaman and Matthew Neeley and Charles Neill and Ani Nersisyan and Michael Newman and Jiun How Ng and Anthony Nguyen and Murray Nguyen and Murphy Yuezhen Niu and Thomas E. O'Brien and Seun Omonije and Andre Petukhov and Rebecca Potter and Leonid P. Pryadko and Chris Quintana and Charles Rocque and Nicholas C. Rubin and Negar Saei and Daniel Sank and Kannan Sankaragomathi and Kevin J. Satzinger and Henry F. Schurkus and Christopher Schuster and Michael J. Shearn and Aaron Shorter and Noah Shutty and Vladimir Shvarts and Jindra Skruzny and W. Clarke Smith and Rolando Somma and George Sterling and Doug Strain and Marco Szalay and Alfredo Torres and Guifre Vidal and Benjamin Villalonga and Catherine Vollgraff Heidweiller and Theodore White and Bryan W. K. Woo and Cheng Xing and Z. Jamie Yao and Ping Yeh and Juhwan Yoo and Grayson Young and Adam Zalcman and Yaxing Zhang and Ningfeng Zhu and Nicholas Zobrist and Hartmut Neven and Sergio Boixo and Anthony Megrant and Julian Kelly and Yu Chen and Vadim Smelyanskiy and Eun-Ah Kim and Igor Aleiner and Pedram Roushan},
journal= {arXiv preprint arXiv:2210.10255},
year = {2023}
}