Scaling and logic in the color code on a superconducting quantum processor
Abstract
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.
Cite
@article{arxiv.2412.14256,
title = {Scaling and logic in the color code on a superconducting quantum processor},
author = {Nathan Lacroix and Alexandre Bourassa and Francisco J. H. Heras and Lei M. Zhang and Johannes Bausch and Andrew W. Senior and Thomas Edlich and Noah Shutty and Volodymyr Sivak and Andreas Bengtsson and Matt McEwen and Oscar Higgott and Dvir Kafri and Jahan Claes and Alexis Morvan and Zijun Chen and Adam Zalcman and Sid Madhuk and Rajeev Acharya and Laleh Aghababaie Beni and Georg Aigeldinger and Ross Alcaraz and Trond I. Andersen and Markus Ansmann and Frank Arute and Kunal Arya and Abraham Asfaw and Juan Atalaya and Ryan Babbush and Brian Ballard and Joseph C. Bardin and Alexander Bilmes and Sam Blackwell and Jenna Bovaird and Dylan Bowers and Leon Brill and Michael Broughton and David A. Browne and Brett Buchea and Bob B. Buckley and Tim Burger and Brian Burkett and Nicholas Bushnell and Anthony Cabrera and Juan Campero and Hung-Shen Chang and Ben Chiaro and Liang-Ying Chih and Agnetta Y. Cleland and Josh Cogan and Roberto Collins and Paul Conner and William Courtney and Alexander L. Crook and Ben Curtin and Sayan Das and Sean Demura and Laura De Lorenzo and Agustin Di Paolo and Paul Donohoe and Ilya Drozdov and Andrew Dunsworth and Alec Eickbusch and Aviv Moshe Elbag and Mahmoud Elzouka and Catherine Erickson and Vinicius S. Ferreira and Leslie Flores Burgos and Ebrahim Forati and Austin G. Fowler and Brooks Foxen and Suhas Ganjam and Gonzalo Garcia and Robert Gasca and Élie Genois and William Giang and Dar Gilboa and Raja Gosula and Alejandro Grajales Dau and Dietrich Graumann and Alex Greene and Jonathan A. Gross and Tan Ha and Steve Habegger and Monica Hansen and Matthew P. Harrigan and Sean D. Harrington and Stephen Heslin and Paula Heu and Reno Hiltermann and Jeremy Hilton and Sabrina Hong and Hsin-Yuan Huang and Ashley Huff and William J. Huggins and Evan Jeffrey and Zhang Jiang and Xiaoxuan Jin and Chaitali Joshi and Pavol Juhas and Andreas Kabel and Hui Kang and Amir H. Karamlou and Kostyantyn Kechedzhi and Trupti Khaire and Tanuj Khattar and Mostafa Khezri and Seon Kim and Paul V. Klimov and Bryce Kobrin and Alexander N. Korotkov and Fedor Kostritsa and John Mark Kreikebaum and Vladislav D. Kurilovich and David Landhuis and Tiano Lange-Dei and Brandon W. Langley and Pavel Laptev and Kim-Ming Lau and Justin Ledford and Kenny Lee and Brian J. Lester and Loïck Le Guevel and Wing Yan Li and Yin Li and Alexander T. Lill and William P. Livingston and Aditya Locharla and Erik Lucero and Daniel Lundahl and Aaron Lunt and Ashley Maloney and Salvatore Mandrà and Leigh S. Martin and Orion Martin and Cameron Maxfield and Jarrod R. McClean and Seneca Meeks and Anthony Megrant and Kevin C. Miao and Reza Molavi and Sebastian Molina and Shirin Montazeri and Ramis Movassagh and Charles Neill and Michael Newman and Anthony Nguyen and Murray Nguyen and Chia-Hung Ni and Murphy Y. Niu and Logan Oas and William D. Oliver and Raymond Orosco and Kristoffer Ottosson and Alex Pizzuto and Rebecca Potter and Orion Pritchard and Chris Quintana and Ganesh Ramachandran and Matthew J. Reagor and Rachel Resnick and David M. Rhodes and Gabrielle Roberts and Eliott Rosenberg and Emma Rosenfeld and Elizabeth Rossi and Pedram Roushan and Kannan Sankaragomathi and Henry F. Schurkus and Michael J. Shearn and Aaron Shorter and Vladimir Shvarts and Spencer Small and W. Clarke Smith and Sofia Springer and George Sterling and Jordan Suchard and Aaron Szasz and Alex Sztein and Douglas Thor and Eifu Tomita and Alfredo Torres and M. Mert Torunbalci and Abeer Vaishnav and Justin Vargas and Sergey Vdovichev and Guifre Vidal and Catherine Vollgraff Heidweiller and Steven Waltman and Jonathan Waltz and Shannon X. Wang and Brayden Ware and Travis Weidel and Theodore White and Kristi Wong and Bryan W. K. Woo and Maddy Woodson and Cheng Xing and Z. Jamie Yao and Ping Yeh and Bicheng Ying and Juhwan Yoo and Noureldin Yosri and Grayson Young and Yaxing Zhang and Ningfeng Zhu and Nicholas Zobrist and Hartmut Neven and Pushmeet Kohli and Alex Davies and Sergio Boixo and Julian Kelly and Cody Jones and Craig Gidney and Kevin J. Satzinger},
journal= {arXiv preprint arXiv:2412.14256},
year = {2026}
}