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Scaling and logic in the color code on a superconducting quantum processor

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Main Authors:	Lacroix, Nathan, Bourassa, Alexandre, Heras, Francisco J. H., Zhang, Lei M., Bausch, Johannes, Senior, Andrew W., Edlich, Thomas, Shutty, Noah, Sivak, Volodymyr, Bengtsson, Andreas, McEwen, Matt, Higgott, Oscar, Kafri, Dvir, Claes, Jahan, Morvan, Alexis, Chen, Zijun, Zalcman, Adam, Madhuk, Sid, Acharya, Rajeev, Beni, Laleh Aghababaie, Aigeldinger, Georg, Alcaraz, Ross, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Babbush, Ryan, Ballard, Brian, Bardin, Joseph C., Bilmes, Alexander, Blackwell, Sam, Bovaird, Jenna, Bowers, Dylan, Brill, Leon, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Cabrera, Anthony, Campero, Juan, Chang, Hung-Shen, Chiaro, Ben, Chih, Liang-Ying, Cleland, Agnetta Y., Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Das, Sayan, Demura, Sean, De Lorenzo, Laura, Di Paolo, Agustin, Donohoe, Paul, Drozdov, Ilya, Dunsworth, Andrew, Eickbusch, Alec, Elbag, Aviv Moshe, Elzouka, Mahmoud, Erickson, Catherine, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Ganjam, Suhas, Garcia, Gonzalo, Gasca, Robert, Genois, Élie, Giang, William, Gilboa, Dar, Gosula, Raja, Dau, Alejandro Grajales, Graumann, Dietrich, Greene, Alex, Gross, Jonathan A., Ha, Tan, Habegger, Steve, Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heslin, Stephen, Heu, Paula, Hiltermann, Reno, Hilton, Jeremy, Hong, Sabrina, Huang, Hsin-Yuan, Huff, Ashley, Huggins, William J., Jeffrey, Evan, Jiang, Zhang, Jin, Xiaoxuan, Joshi, Chaitali, Juhas, Pavol, Kabel, Andreas, Kang, Hui, Karamlou, Amir H., Kechedzhi, Kostyantyn, Khaire, Trupti, Khattar, Tanuj, Khezri, Mostafa, Kim, Seon, Klimov, Paul V., Kobrin, Bryce, Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Kurilovich, Vladislav D., Landhuis, David, Lange-Dei, Tiano, Langley, Brandon W., Laptev, Pavel, Lau, Kim-Ming, Ledford, Justin, Lee, Kenny, Lester, Brian J., Guevel, Loïck Le, Li, Wing Yan, Li, Yin, Lill, Alexander T., Livingston, William P., Locharla, Aditya, Lucero, Erik, Lundahl, Daniel, Lunt, Aaron, Maloney, Ashley, Mandrà, Salvatore, Martin, Leigh S., Martin, Orion, Maxfield, Cameron, McClean, Jarrod R., Meeks, Seneca, Megrant, Anthony, Miao, Kevin C., Molavi, Reza, Molina, Sebastian, Montazeri, Shirin, Movassagh, Ramis, Neill, Charles, Newman, Michael, Nguyen, Anthony, Nguyen, Murray, Ni, Chia-Hung, Niu, Murphy Y., Oas, Logan, Oliver, William D., Orosco, Raymond, Ottosson, Kristoffer, Pizzuto, Alex, Potter, Rebecca, Pritchard, Orion, Quintana, Chris, Ramachandran, Ganesh, Reagor, Matthew J., Resnick, Rachel, Rhodes, David M., Roberts, Gabrielle, Rosenberg, Eliott, Rosenfeld, Emma, Rossi, Elizabeth, Roushan, Pedram, Sankaragomathi, Kannan, Schurkus, Henry F., Shearn, Michael J., Shorter, Aaron, Shvarts, Vladimir, Small, Spencer, Smith, W. Clarke, Springer, Sofia, Sterling, George, Suchard, Jordan, Szasz, Aaron, Sztein, Alex, Thor, Douglas, Tomita, Eifu, Torres, Alfredo, Torunbalci, M. Mert, Vaishnav, Abeer, Vargas, Justin, Vdovichev, Sergey, Vidal, Guifre, Heidweiller, Catherine Vollgraff, Waltman, Steven, Waltz, Jonathan, Wang, Shannon X., Ware, Brayden, Weidel, Travis, White, Theodore, Wong, Kristi, Woo, Bryan W. K., Woodson, Maddy, Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Ying, Bicheng, Yoo, Juhwan, Yosri, Noureldin, Young, Grayson, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Hartmut, Kohli, Pushmeet, Davies, Alex, Boixo, Sergio, Kelly, Julian, Jones, Cody, Gidney, Craig, Satzinger, Kevin J.
Format:	Preprint
Published:	2024
Subjects:	Quantum Physics
Online Access:	Acceder al recurso
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author	Lacroix, Nathan Bourassa, Alexandre Heras, Francisco J. H. Zhang, Lei M. Bausch, Johannes Senior, Andrew W. Edlich, Thomas Shutty, Noah Sivak, Volodymyr Bengtsson, Andreas McEwen, Matt Higgott, Oscar Kafri, Dvir Claes, Jahan Morvan, Alexis Chen, Zijun Zalcman, Adam Madhuk, Sid Acharya, Rajeev Beni, Laleh Aghababaie Aigeldinger, Georg Alcaraz, Ross Andersen, Trond I. Ansmann, Markus Arute, Frank Arya, Kunal Asfaw, Abraham Atalaya, Juan Babbush, Ryan Ballard, Brian Bardin, Joseph C. Bilmes, Alexander Blackwell, Sam Bovaird, Jenna Bowers, Dylan Brill, Leon Broughton, Michael Browne, David A. Buchea, Brett Buckley, Bob B. Burger, Tim Burkett, Brian Bushnell, Nicholas Cabrera, Anthony Campero, Juan Chang, Hung-Shen Chiaro, Ben Chih, Liang-Ying Cleland, Agnetta Y. Cogan, Josh Collins, Roberto Conner, Paul Courtney, William Crook, Alexander L. Curtin, Ben Das, Sayan Demura, Sean De Lorenzo, Laura Di Paolo, Agustin Donohoe, Paul Drozdov, Ilya Dunsworth, Andrew Eickbusch, Alec Elbag, Aviv Moshe Elzouka, Mahmoud Erickson, Catherine Ferreira, Vinicius S. Burgos, Leslie Flores Forati, Ebrahim Fowler, Austin G. Foxen, Brooks Ganjam, Suhas Garcia, Gonzalo Gasca, Robert Genois, Élie Giang, William Gilboa, Dar Gosula, Raja Dau, Alejandro Grajales Graumann, Dietrich Greene, Alex Gross, Jonathan A. Ha, Tan Habegger, Steve Hansen, Monica Harrigan, Matthew P. Harrington, Sean D. Heslin, Stephen Heu, Paula Hiltermann, Reno Hilton, Jeremy Hong, Sabrina Huang, Hsin-Yuan Huff, Ashley Huggins, William J. Jeffrey, Evan Jiang, Zhang Jin, Xiaoxuan Joshi, Chaitali Juhas, Pavol Kabel, Andreas Kang, Hui Karamlou, Amir H. Kechedzhi, Kostyantyn Khaire, Trupti Khattar, Tanuj Khezri, Mostafa Kim, Seon Klimov, Paul V. Kobrin, Bryce Korotkov, Alexander N. Kostritsa, Fedor Kreikebaum, John Mark Kurilovich, Vladislav D. Landhuis, David Lange-Dei, Tiano Langley, Brandon W. Laptev, Pavel Lau, Kim-Ming Ledford, Justin Lee, Kenny Lester, Brian J. Guevel, Loïck Le Li, Wing Yan Li, Yin Lill, Alexander T. Livingston, William P. Locharla, Aditya Lucero, Erik Lundahl, Daniel Lunt, Aaron Maloney, Ashley Mandrà, Salvatore Martin, Leigh S. Martin, Orion Maxfield, Cameron McClean, Jarrod R. Meeks, Seneca Megrant, Anthony Miao, Kevin C. Molavi, Reza Molina, Sebastian Montazeri, Shirin Movassagh, Ramis Neill, Charles Newman, Michael Nguyen, Anthony Nguyen, Murray Ni, Chia-Hung Niu, Murphy Y. Oas, Logan Oliver, William D. Orosco, Raymond Ottosson, Kristoffer Pizzuto, Alex Potter, Rebecca Pritchard, Orion Quintana, Chris Ramachandran, Ganesh Reagor, Matthew J. Resnick, Rachel Rhodes, David M. Roberts, Gabrielle Rosenberg, Eliott Rosenfeld, Emma Rossi, Elizabeth Roushan, Pedram Sankaragomathi, Kannan Schurkus, Henry F. Shearn, Michael J. Shorter, Aaron Shvarts, Vladimir Small, Spencer Smith, W. Clarke Springer, Sofia Sterling, George Suchard, Jordan Szasz, Aaron Sztein, Alex Thor, Douglas Tomita, Eifu Torres, Alfredo Torunbalci, M. Mert Vaishnav, Abeer Vargas, Justin Vdovichev, Sergey Vidal, Guifre Heidweiller, Catherine Vollgraff Waltman, Steven Waltz, Jonathan Wang, Shannon X. Ware, Brayden Weidel, Travis White, Theodore Wong, Kristi Woo, Bryan W. K. Woodson, Maddy Xing, Cheng Yao, Z. Jamie Yeh, Ping Ying, Bicheng Yoo, Juhwan Yosri, Noureldin Young, Grayson Zhang, Yaxing Zhu, Ningfeng Zobrist, Nicholas Neven, Hartmut Kohli, Pushmeet Davies, Alex Boixo, Sergio Kelly, Julian Jones, Cody Gidney, Craig Satzinger, Kevin J.
author_facet	Lacroix, Nathan Bourassa, Alexandre Heras, Francisco J. H. Zhang, Lei M. Bausch, Johannes Senior, Andrew W. Edlich, Thomas Shutty, Noah Sivak, Volodymyr Bengtsson, Andreas McEwen, Matt Higgott, Oscar Kafri, Dvir Claes, Jahan Morvan, Alexis Chen, Zijun Zalcman, Adam Madhuk, Sid Acharya, Rajeev Beni, Laleh Aghababaie Aigeldinger, Georg Alcaraz, Ross Andersen, Trond I. Ansmann, Markus Arute, Frank Arya, Kunal Asfaw, Abraham Atalaya, Juan Babbush, Ryan Ballard, Brian Bardin, Joseph C. Bilmes, Alexander Blackwell, Sam Bovaird, Jenna Bowers, Dylan Brill, Leon Broughton, Michael Browne, David A. Buchea, Brett Buckley, Bob B. Burger, Tim Burkett, Brian Bushnell, Nicholas Cabrera, Anthony Campero, Juan Chang, Hung-Shen Chiaro, Ben Chih, Liang-Ying Cleland, Agnetta Y. Cogan, Josh Collins, Roberto Conner, Paul Courtney, William Crook, Alexander L. Curtin, Ben Das, Sayan Demura, Sean De Lorenzo, Laura Di Paolo, Agustin Donohoe, Paul Drozdov, Ilya Dunsworth, Andrew Eickbusch, Alec Elbag, Aviv Moshe Elzouka, Mahmoud Erickson, Catherine Ferreira, Vinicius S. Burgos, Leslie Flores Forati, Ebrahim Fowler, Austin G. Foxen, Brooks Ganjam, Suhas Garcia, Gonzalo Gasca, Robert Genois, Élie Giang, William Gilboa, Dar Gosula, Raja Dau, Alejandro Grajales Graumann, Dietrich Greene, Alex Gross, Jonathan A. Ha, Tan Habegger, Steve Hansen, Monica Harrigan, Matthew P. Harrington, Sean D. Heslin, Stephen Heu, Paula Hiltermann, Reno Hilton, Jeremy Hong, Sabrina Huang, Hsin-Yuan Huff, Ashley Huggins, William J. Jeffrey, Evan Jiang, Zhang Jin, Xiaoxuan Joshi, Chaitali Juhas, Pavol Kabel, Andreas Kang, Hui Karamlou, Amir H. Kechedzhi, Kostyantyn Khaire, Trupti Khattar, Tanuj Khezri, Mostafa Kim, Seon Klimov, Paul V. Kobrin, Bryce Korotkov, Alexander N. Kostritsa, Fedor Kreikebaum, John Mark Kurilovich, Vladislav D. Landhuis, David Lange-Dei, Tiano Langley, Brandon W. Laptev, Pavel Lau, Kim-Ming Ledford, Justin Lee, Kenny Lester, Brian J. Guevel, Loïck Le Li, Wing Yan Li, Yin Lill, Alexander T. Livingston, William P. Locharla, Aditya Lucero, Erik Lundahl, Daniel Lunt, Aaron Maloney, Ashley Mandrà, Salvatore Martin, Leigh S. Martin, Orion Maxfield, Cameron McClean, Jarrod R. Meeks, Seneca Megrant, Anthony Miao, Kevin C. Molavi, Reza Molina, Sebastian Montazeri, Shirin Movassagh, Ramis Neill, Charles Newman, Michael Nguyen, Anthony Nguyen, Murray Ni, Chia-Hung Niu, Murphy Y. Oas, Logan Oliver, William D. Orosco, Raymond Ottosson, Kristoffer Pizzuto, Alex Potter, Rebecca Pritchard, Orion Quintana, Chris Ramachandran, Ganesh Reagor, Matthew J. Resnick, Rachel Rhodes, David M. Roberts, Gabrielle Rosenberg, Eliott Rosenfeld, Emma Rossi, Elizabeth Roushan, Pedram Sankaragomathi, Kannan Schurkus, Henry F. Shearn, Michael J. Shorter, Aaron Shvarts, Vladimir Small, Spencer Smith, W. Clarke Springer, Sofia Sterling, George Suchard, Jordan Szasz, Aaron Sztein, Alex Thor, Douglas Tomita, Eifu Torres, Alfredo Torunbalci, M. Mert Vaishnav, Abeer Vargas, Justin Vdovichev, Sergey Vidal, Guifre Heidweiller, Catherine Vollgraff Waltman, Steven Waltz, Jonathan Wang, Shannon X. Ware, Brayden Weidel, Travis White, Theodore Wong, Kristi Woo, Bryan W. K. Woodson, Maddy Xing, Cheng Yao, Z. Jamie Yeh, Ping Ying, Bicheng Yoo, Juhwan Yosri, Noureldin Young, Grayson Zhang, Yaxing Zhu, Ningfeng Zobrist, Nicholas Neven, Hartmut Kohli, Pushmeet Davies, Alex Boixo, Sergio Kelly, Julian Jones, Cody Gidney, Craig Satzinger, Kevin J.
contents	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 $Λ_{3/5}$ = 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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2412_14256
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Scaling and logic in the color code on a superconducting quantum processor Lacroix, Nathan Bourassa, Alexandre Heras, Francisco J. H. Zhang, Lei M. Bausch, Johannes Senior, Andrew W. Edlich, Thomas Shutty, Noah Sivak, Volodymyr Bengtsson, Andreas McEwen, Matt Higgott, Oscar Kafri, Dvir Claes, Jahan Morvan, Alexis Chen, Zijun Zalcman, Adam Madhuk, Sid Acharya, Rajeev Beni, Laleh Aghababaie Aigeldinger, Georg Alcaraz, Ross Andersen, Trond I. Ansmann, Markus Arute, Frank Arya, Kunal Asfaw, Abraham Atalaya, Juan Babbush, Ryan Ballard, Brian Bardin, Joseph C. Bilmes, Alexander Blackwell, Sam Bovaird, Jenna Bowers, Dylan Brill, Leon Broughton, Michael Browne, David A. Buchea, Brett Buckley, Bob B. Burger, Tim Burkett, Brian Bushnell, Nicholas Cabrera, Anthony Campero, Juan Chang, Hung-Shen Chiaro, Ben Chih, Liang-Ying Cleland, Agnetta Y. Cogan, Josh Collins, Roberto Conner, Paul Courtney, William Crook, Alexander L. Curtin, Ben Das, Sayan Demura, Sean De Lorenzo, Laura Di Paolo, Agustin Donohoe, Paul Drozdov, Ilya Dunsworth, Andrew Eickbusch, Alec Elbag, Aviv Moshe Elzouka, Mahmoud Erickson, Catherine Ferreira, Vinicius S. Burgos, Leslie Flores Forati, Ebrahim Fowler, Austin G. Foxen, Brooks Ganjam, Suhas Garcia, Gonzalo Gasca, Robert Genois, Élie Giang, William Gilboa, Dar Gosula, Raja Dau, Alejandro Grajales Graumann, Dietrich Greene, Alex Gross, Jonathan A. Ha, Tan Habegger, Steve Hansen, Monica Harrigan, Matthew P. Harrington, Sean D. Heslin, Stephen Heu, Paula Hiltermann, Reno Hilton, Jeremy Hong, Sabrina Huang, Hsin-Yuan Huff, Ashley Huggins, William J. Jeffrey, Evan Jiang, Zhang Jin, Xiaoxuan Joshi, Chaitali Juhas, Pavol Kabel, Andreas Kang, Hui Karamlou, Amir H. Kechedzhi, Kostyantyn Khaire, Trupti Khattar, Tanuj Khezri, Mostafa Kim, Seon Klimov, Paul V. Kobrin, Bryce Korotkov, Alexander N. Kostritsa, Fedor Kreikebaum, John Mark Kurilovich, Vladislav D. Landhuis, David Lange-Dei, Tiano Langley, Brandon W. Laptev, Pavel Lau, Kim-Ming Ledford, Justin Lee, Kenny Lester, Brian J. Guevel, Loïck Le Li, Wing Yan Li, Yin Lill, Alexander T. Livingston, William P. Locharla, Aditya Lucero, Erik Lundahl, Daniel Lunt, Aaron Maloney, Ashley Mandrà, Salvatore Martin, Leigh S. Martin, Orion Maxfield, Cameron McClean, Jarrod R. Meeks, Seneca Megrant, Anthony Miao, Kevin C. Molavi, Reza Molina, Sebastian Montazeri, Shirin Movassagh, Ramis Neill, Charles Newman, Michael Nguyen, Anthony Nguyen, Murray Ni, Chia-Hung Niu, Murphy Y. Oas, Logan Oliver, William D. Orosco, Raymond Ottosson, Kristoffer Pizzuto, Alex Potter, Rebecca Pritchard, Orion Quintana, Chris Ramachandran, Ganesh Reagor, Matthew J. Resnick, Rachel Rhodes, David M. Roberts, Gabrielle Rosenberg, Eliott Rosenfeld, Emma Rossi, Elizabeth Roushan, Pedram Sankaragomathi, Kannan Schurkus, Henry F. Shearn, Michael J. Shorter, Aaron Shvarts, Vladimir Small, Spencer Smith, W. Clarke Springer, Sofia Sterling, George Suchard, Jordan Szasz, Aaron Sztein, Alex Thor, Douglas Tomita, Eifu Torres, Alfredo Torunbalci, M. Mert Vaishnav, Abeer Vargas, Justin Vdovichev, Sergey Vidal, Guifre Heidweiller, Catherine Vollgraff Waltman, Steven Waltz, Jonathan Wang, Shannon X. Ware, Brayden Weidel, Travis White, Theodore Wong, Kristi Woo, Bryan W. K. Woodson, Maddy Xing, Cheng Yao, Z. Jamie Yeh, Ping Ying, Bicheng Yoo, Juhwan Yosri, Noureldin Young, Grayson Zhang, Yaxing Zhu, Ningfeng Zobrist, Nicholas Neven, Hartmut Kohli, Pushmeet Davies, Alex Boixo, Sergio Kelly, Julian Jones, Cody Gidney, Craig Satzinger, Kevin J. Quantum Physics 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 $Λ_{3/5}$ = 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.
title	Scaling and logic in the color code on a superconducting quantum processor
topic	Quantum Physics
url	https://arxiv.org/abs/2412.14256