Author: "Schurkus, Henry" - Searchworks@Jio Institute Digital Library Search Results

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27 results on '"Schurkus, Henry"'

1. Demonstrating dynamic surface codes

Author: Eickbusch, Alec, McEwen, Matt, Sivak, Volodymyr, Bourassa, Alexandre, Atalaya, Juan, Claes, Jahan, Kafri, Dvir, Gidney, Craig, Warren, Christopher W., Gross, Jonathan, Opremcak, Alex, Miao, Nicholas Zobrist Kevin C., Roberts, Gabrielle, Satzinger, Kevin J., Bengtsson, Andreas, Neeley, Matthew, Livingston, William P., Greene, Alex, Rajeev, Acharya, Beni, Laleh Aghababaie, Aigeldinger, Georg, Alcaraz, Ross, Andersen, Trond I., Ansmann, Markus, Frank, Arute, Arya, Kunal, Asfaw, Abraham, Babbush, Ryan, Ballard, Brian, Bardin, Joseph C., Bilmes, Alexander, Jenna, Bovaird, Bowers, Dylan, Brill, Leon, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Tim, Burger, 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, Alexander, Crook, L., Curtin, Ben, Das, Sayan, Barba, Alexander Del Toro, Demura, Sean, De Lorenzo, Laura, Di Paolo, Agustin, Donohoe, Paul, Drozdov, Ilya K., Dunsworth, Andrew, Elbag, Aviv Moshe, Elzouka, Mahmoud, Erickson, Catherine, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Ganjam, Suhas, Gonzalo, Garcia, Gasca, Robert, Genois, Élie, Giang, William, Gilboa, Dar, Gosula, Raja, Dau, Alejandro Grajales, Dietrich, Graumann, Ha, Tan, Habegger, Steve, Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heslin, Stephen, Heu, Paula, Higgott, Oscar, Hiltermann, Reno, Hilton, Jeremy, Huang, Hsin-Yuan, Huff, Ashley, Huggins, William J., Jeffrey, Evan, Jiang, Zhang, Jin, Xiaoxuan, Jones, Cody, Joshi, Chaitali, Juhas, Pavol, Kabel, Andreas, Kang, Hui, Amir, Karamlou, H., Kechedzhi, Kostyantyn, Khaire, Trupti, Khattar, Tanuj, Khezri, Mostafa, Kim, Seon, Kobrin, Bryce, Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Kurilovich, Vladislav D., Landhuis, David, Tiano, Lange-Dei, Langley, Brandon W., Lau, Kim-Ming, Ledford, Justin, Lee, Kenny, Lester, Brian J., Guevel, Loïck Le, Wing, Li, Yan, Lill, Alexander T., Locharla, Aditya, Lucero, Erik, Lundahl, Daniel, Lunt, Aaron, Madhuk, Sid, Maloney, Ashley, Mandrà, Salvatore, Martin, Leigh S., Martin, Orion, Maxfield, Cameron, McClean, Jarrod R., Meeks, Seneca, Anthony, Megrant, Molavi, Reza, Molina, Sebastian, Montazeri, Shirin, Movassagh, Ramis, Newman, Michael, Nguyen, Anthony, Nguyen, Murray, Ni, Chia-Hung, Oas, Logan, Orosco, Raymond, Ottosson, Kristoffer, Pizzuto, Alex, Potter, Rebecca, Pritchard, Orion, Quintana, Chris, Ramachandran, Ganesh, Reagor, Matthew J., Rhodes, David M., Rosenberg, Eliott, Rossi, Elizabeth, Sankaragomathi, Kannan, Schurkus, Henry F., Shearn, Michael J., Shorter, Aaron, Shutty, Noah, 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, Sergey, Vdovichev, 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, Zalcman, Adam, Yaxing, Zhang, Zhu, Ningfeng, Boixo, Sergio, Kelly, Julian, Smelyanskiy, Vadim, Neven, Hartmut, Bacon, Dave, Chen, Zijun, Klimov, Paul V., Roushan, Pedram, Neill, Charles, Chen, Yu, and Morvan, Alexis
Subjects: Quantum Physics
Abstract: A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of $\Lambda_{35,\text{hex}} = 2.15(2)$, $\Lambda_{35,\text{walk}} = 1.69(6)$, and $\Lambda_{35,\text{iSWAP}} = 1.56(2)$, achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design., Comment: 11 pages, 5 figures, Supplementary Information
Published: 2024

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

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, and Satzinger, Kevin J.
Subjects: Quantum Physics
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 $\Lambda_{3/5}$ = 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.
Published: 2024

3. Observation of disorder-free localization and efficient disorder averaging on a quantum processor

Author: Gyawali, Gaurav, Cochran, Tyler, Lensky, Yuri, Rosenberg, Eliott, Karamlou, Amir H., Kechedzhi, Kostyantyn, Berndtsson, Julia, Westerhout, Tom, Asfaw, Abraham, Abanin, Dmitry, Acharya, Rajeev, Beni, Laleh Aghababaie, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Astrakhantsev, Nikita, Atalaya, Juan, Babbush, Ryan, Ballard, Brian, Bardin, Joseph C., Bengtsson, Andreas, Bilmes, Alexander, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Cabrera, Anthony, Campero, Juan, Chang, Hung-Shen, Chen, Zijun, Chiaro, Ben, Claes, Jahan, Cleland, Agnetta Y., Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Das, Sayan, Debroy, Dripto M., De Lorenzo, Laura, Barba, Alexander Del Toro, Demura, Sean, Di Paolo, Agustin, Donohoe, Paul, Drozdov, Ilya, Dunsworth, Andrew, Earle, Clint, Eickbusch, Alec, Elbag, Aviv Moshe, Elzouka, Mahmoud, Erickson, Catherine, Faoro, Lara, Fatemi, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Ganjam, Suhas, Gasca, Robert, Giang, William, Gidney, Craig, Gilboa, Dar, Gosula, Raja, Dau, Alejandro Grajales, Graumann, Dietrich, Greene, Alex, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heslin, Stephen, Heu, Paula, Hill, Gordon, Hilton, Jeremy, Hoffmann, Markus R., Huang, Hsin-Yuan, Huff, Ashley, Huggins, William J., Ioffe, Lev B., Isakov, Sergei V., Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Jordan, Stephen, Joshi, Chaitali, Juhas, Pavol, Kafri, Dvir, Kang, Hui, Khaire, Trupti, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Klimov, Paul V., Klots, Andrey R., 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, Guevel, Loïck Le, Ledford, Justin, Lee, Joonho, Lee, Kenny, Lester, Brian J., Li, Wing Yan, Lill, Alexander T., Liu, Wayne, Livingston, William P., Locharla, Aditya, Lundahl, Daniel, Lunt, Aaron, Madhuk, Sid, Maloney, Ashley, Mandrà, Salvatore, Martin, Leigh S., Martin, Steven, Martin, Orion, Maxfield, Cameron, McClean, Jarrod R., McEwen, Matt, Meeks, Seneca, Megrant, Anthony, Mi, Xiao, Miao, Kevin C., Mieszala, Amanda, Molina, Sebastian, Montazeri, Shirin, Morvan, Alexis, Movassagh, Ramis, Neill, Charles, Nersisyan, Ani, Newman, Michael, Nguyen, Anthony, Nguyen, Murray, Ni, Chia-Hung, Niu, Murphy Yuezhen, Oliver, William D., Ottosson, Kristoffer, Pizzuto, Alex, Potter, Rebecca, Pritchard, Orion, Pryadko, Leonid P., Quintana, Chris, Reagor, Matthew J., Rhodes, David M., Roberts, Gabrielle, Rocque, Charles, Rubin, Nicholas C., Saei, Negar, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Sivak, Volodymyr, Skruzny, Jindra, Small, Spencer, Smith, W. Clarke, Springer, Sofia, Sterling, George, Suchard, Jordan, Szalay, Marco, Szasz, Aaron, Sztein, Alex, Thor, Douglas, Torunbalci, M. Mert, Vaishnav, Abeer, Vdovichev, Sergey, Vidal, Guifré, Heidweiller, Catherine Vollgraff, Waltman, Steven, Wang, Shannon X., White, Theodore, Wong, Kristi, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Ying, Bicheng, Yoo, Juhwan, Yosri, Noureldin, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Boixo, Sergio, Kelly, Julian, Lucero, Erik, Chen, Yu, Smelyanskiy, Vadim, Neven, Hartmut, Kovrizhin, Dmitry, Knolle, Johannes, Halimeh, Jad C., Aleiner, Igor, Moessner, Roderich, and Roushan, Pedram
Subjects: Quantum Physics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Lattice
Abstract: One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.
Published: 2024

4. Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

Author: Cochran, Tyler A., Jobst, Bernhard, Rosenberg, Eliott, Lensky, Yuri D., Gyawali, Gaurav, Eassa, Norhan, Will, Melissa, Abanin, Dmitry, Acharya, Rajeev, Beni, Laleh Aghababaie, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Babbush, Ryan, Ballard, Brian, Bardin, Joseph C., Bengtsson, Andreas, Bilmes, Alexander, Bourassa, Alexandre, Bovaird, Jenna, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Cabrera, Anthony, Campero, Juan, Chang, Hung-Shen, Chen, Zijun, Chiaro, Ben, Claes, Jahan, 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, Gasca, Robert, Genois, Élie, Giang, William, Gilboa, Dar, Gosula, Raja, Dau, Alejandro Grajales, Graumann, Dietrich, Greene, Alex, Gross, Jonathan A., Habegger, Steve, Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heu, Paula, Higgott, Oscar, Hilton, Jeremy, Huang, Hsin-Yuan, Huff, Ashley, Huggins, William J., Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Joshi, Chaitali, Juhas, Pavol, Kafri, Dvir, 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., Lau, Kim-Ming, Ledford, Justin, Lee, Kenny, Lester, Brian J., Guevel, Loïck Le, Li, Wing Yan, Lill, Alexander T., Livingston, William P., Locharla, Aditya, Lundahl, Daniel, Lunt, Aaron, Madhuk, Sid, Maloney, Ashley, Mandrà, Salvatore, Martin, Leigh S., Martin, Orion, Maxfield, Cameron, McClean, Jarrod R., McEwen, Matt, 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 Yuezhen, Oliver, William D., Ottosson, Kristoffer, Pizzuto, Alex, Potter, Rebecca, Pritchard, Orion, Quintana, Chris, Ramachandran, Ganesh, Reagor, Matthew J., Rhodes, David M., Roberts, Gabrielle, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Sivak, Volodymyr, Small, Spencer, Smith, W. Clarke, Springer, Sofia, Sterling, George, Suchard, Jordan, Szasz, Aaron, Sztein, Alex, Thor, Douglas, Torunbalci, M. Mert, Vaishnav, Abeer, Vargas, Justin, Vdovichev, Sergey, Vidal, Guifre, Heidweiller, Catherine Vollgraff, Waltman, Steven, Wang, Shannon X., Ware, Brayden, White, Theodore, Wong, Kristi, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Ying, Bicheng, Yoo, Juhwan, Yosri, Noureldin, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobris, Nicholas, Boixo, Sergio, Kelly, Julian, Lucero, Erik, Chen, Yu, Smelyanskiy, Vadim, Neven, Hartmut, Gammon-Smith, Adam, Pollmann, Frank, Knap, Michael, and Roushan, Pedram
Subjects: Quantum Physics, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Lattice
Abstract: Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics.
Published: 2024

5. Quantum error correction below the surface code threshold

Author: Acharya, Rajeev, Aghababaie-Beni, Laleh, Aleiner, Igor, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Astrakhantsev, Nikita, Atalaya, Juan, Babbush, Ryan, Bacon, Dave, Ballard, Brian, Bardin, Joseph C., Bausch, Johannes, Bengtsson, Andreas, Bilmes, Alexander, Blackwell, Sam, Boixo, Sergio, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Cabrera, Anthony, Campero, Juan, Chang, Hung-Shen, Chen, Yu, Chen, Zijun, Chiaro, Ben, Chik, Desmond, Chou, Charina, Claes, Jahan, Cleland, Agnetta Y., Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Das, Sayan, Davies, Alex, De Lorenzo, Laura, Debroy, Dripto M., Demura, Sean, Devoret, Michel, Di Paolo, Agustin, Donohoe, Paul, Drozdov, Ilya, Dunsworth, Andrew, Earle, Clint, Edlich, Thomas, Eickbusch, Alec, Elbag, Aviv Moshe, Elzouka, Mahmoud, Erickson, Catherine, Faoro, Lara, Farhi, Edward, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Ganjam, Suhas, Garcia, Gonzalo, Gasca, Robert, Genois, Élie, Giang, William, Gidney, Craig, Gilboa, Dar, Gosula, Raja, Dau, Alejandro Grajales, Graumann, Dietrich, Greene, Alex, Gross, Jonathan A., Habegger, Steve, Hall, John, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heras, Francisco J. H., Heslin, Stephen, Heu, Paula, Higgott, Oscar, Hill, Gordon, Hilton, Jeremy, Holland, George, Hong, Sabrina, Huang, Hsin-Yuan, Huff, Ashley, Huggins, William J., Ioffe, Lev B., Isakov, Sergei V., Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Jordan, Stephen, Joshi, Chaitali, Juhas, Pavol, Kafri, Dvir, Kang, Hui, Karamlou, Amir H., Kechedzhi, Kostyantyn, Kelly, Julian, Khaire, Trupti, Khattar, Tanuj, Khezri, Mostafa, Kim, Seon, Klimov, Paul V., Klots, Andrey R., Kobrin, Bryce, Kohli, Pushmeet, Korotkov, Alexander N., Kostritsa, Fedor, Kothari, Robin, Kozlovskii, Borislav, Kreikebaum, John Mark, Kurilovich, Vladislav D., Lacroix, Nathan, Landhuis, David, Lange-Dei, Tiano, Langley, Brandon W., Laptev, Pavel, Lau, Kim-Ming, Guevel, Loïck Le, Ledford, Justin, Lee, Kenny, Lensky, Yuri D., Leon, Shannon, Lester, Brian J., Li, Wing Yan, Li, Yin, Lill, Alexander T., Liu, Wayne, Livingston, William P., Locharla, Aditya, Lucero, Erik, Lundahl, Daniel, Lunt, Aaron, Madhuk, Sid, Malone, Fionn D., Maloney, Ashley, Mandrá, Salvatore, Martin, Leigh S., Martin, Steven, Martin, Orion, Maxfield, Cameron, McClean, Jarrod R., McEwen, Matt, Meeks, Seneca, Megrant, Anthony, Mi, Xiao, Miao, Kevin C., Mieszala, Amanda, Molavi, Reza, Molina, Sebastian, Montazeri, Shirin, Morvan, Alexis, Movassagh, Ramis, Mruczkiewicz, Wojciech, Naaman, Ofer, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Neven, Hartmut, Newman, Michael, Ng, Jiun How, Nguyen, Anthony, Nguyen, Murray, Ni, Chia-Hung, O'Brien, Thomas E., Oliver, William D., Opremcak, Alex, Ottosson, Kristoffer, Petukhov, Andre, Pizzuto, Alex, Platt, John, Potter, Rebecca, Pritchard, Orion, Pryadko, Leonid P., Quintana, Chris, Ramachandran, Ganesh, Reagor, Matthew J., Rhodes, David M., Roberts, Gabrielle, Rosenberg, Eliott, Rosenfeld, Emma, Roushan, Pedram, Rubin, Nicholas C., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Senior, Andrew W., Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Singh, Shraddha, Sivak, Volodymyr, Skruzny, Jindra, Small, Spencer, Smelyanskiy, Vadim, Smith, W. Clarke, Somma, Rolando D., Springer, Sofia, Sterling, George, Strain, Doug, Suchard, Jordan, Szasz, Aaron, Sztein, Alex, Thor, Douglas, Torres, Alfredo, Torunbalci, M. Mert, Vaishnav, Abeer, Vargas, Justin, Vdovichev, Sergey, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, Waltman, Steven, Wang, Shannon X., Ware, Brayden, Weber, Kate, White, Theodore, Wong, Kristi, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Ying, Bicheng, Yoo, Juhwan, Yosri, Noureldin, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, and Zobrist, Nicholas
Subjects: Quantum Physics
Abstract: Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information
Published: 2024

6. Thermalization and Criticality on an Analog-Digital Quantum Simulator

Author: Andersen, Trond I., Astrakhantsev, Nikita, Karamlou, Amir H., Berndtsson, Julia, Motruk, Johannes, Szasz, Aaron, Gross, Jonathan A., Schuckert, Alexander, Westerhout, Tom, Zhang, Yaxing, Forati, Ebrahim, Rossi, Dario, Kobrin, Bryce, Di Paolo, Agustin, Klots, Andrey R., Drozdov, Ilya, Kurilovich, Vladislav D., Petukhov, Andre, Ioffe, Lev B., Elben, Andreas, Rath, Aniket, Vitale, Vittorio, Vermersch, Benoit, Acharya, Rajeev, Beni, Laleh Aghababaie, Anderson, Kyle, Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Ballard, Brian, Bardin, Joseph C., Bengtsson, Andreas, Bilmes, Alexander, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Browne, David A., Buchea, Brett, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Cabrera, Anthony, Campero, Juan, Chang, Hung-Shen, Chen, Zijun, Chiaro, Ben, Claes, Jahan, Cleland, Agnetta Y., Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Das, Sayan, Debroy, Dripto M., De Lorenzo, Laura, Barba, Alexander Del Toro, Demura, Sean, Donohoe, Paul, Dunsworth, Andrew, Earle, Clint, Eickbusch, Alec, Elbag, Aviv Moshe, Elzouka, Mahmoud, Erickson, Catherine, Faoro, Lara, Fatemi, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Fowler, Austin G., Foxen, Brooks, Ganjam, Suhas, Gasca, Robert, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Gosula, Raja, Dau, Alejandro Grajales, Graumann, Dietrich, Greene, Alex, Habegger, Steve, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heslin, Stephen, Heu, Paula, Hill, Gordon, Hoffmann, Markus R., Huang, Hsin-Yuan, Huang, Trent, Huff, Ashley, Huggins, William J., Isakov, Sergei V., Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Jordan, Stephen, Joshi, Chaitali, Juhas, Pavol, Kafri, Dvir, Kang, Hui, Kechedzhi, Kostyantyn, Khaire, Trupti, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Langley, Brandon W., Laptev, Pavel, Lau, Kim-Ming, Guevel, Loïck Le, Ledford, Justin, Lee, Joonho, Lee, Kenny, Lensky, Yuri D., Lester, Brian J., Li, Wing Yan, Lill, Alexander T., Liu, Wayne, Livingston, William P., Locharla, Aditya, Lundahl, Daniel, Lunt, Aaron, Madhuk, Sid, Maloney, Ashley, Mandrà, Salvatore, Martin, Leigh S., Martin, Orion, Martin, Steven, Maxfield, Cameron, McClean, Jarrod R., McEwen, Matt, Meeks, Seneca, Miao, Kevin C., Mieszala, Amanda, Molina, Sebastian, Montazeri, Shirin, Morvan, Alexis, Movassagh, Ramis, Neill, Charles, Nersisyan, Ani, Newman, Michael, Nguyen, Anthony, Nguyen, Murray, Ni, Chia-Hung, Niu, Murphy Yuezhen, Oliver, William D., Ottosson, Kristoffer, Pizzuto, Alex, Potter, Rebecca, Pritchard, Orion, Pryadko, Leonid P., Quintana, Chris, Reagor, Matthew J., Rhodes, David M., Roberts, Gabrielle, Rocque, Charles, Rosenberg, Eliott, Rubin, Nicholas C., Saei, Negar, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Sivak, Volodymyr, Skruzny, Jindra, Small, Spencer, Smith, W. Clarke, Springer, Sofia, Sterling, George, Suchard, Jordan, Szalay, Marco, Sztein, Alex, Thor, Douglas, Torres, Alfredo, Torunbalci, M. Mert, Vaishnav, Abeer, Vdovichev, Sergey, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, Waltman, Steven, Wang, Shannon X., White, Theodore, Wong, Kristi, Woo, Bryan W., Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Ying, Bicheng, Yoo, Juhwan, Yosri, Noureldin, Young, Grayson, Zalcman, Adam, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Hartmut, Babbush, Ryan, Boixo, Sergio, Hilton, Jeremy, Lucero, Erik, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Vidal, Guifre, Roushan, Pedram, Lauchli, Andreas M., Abanin, Dmitry A., and Mi, Xiao
Subjects: Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Strongly Correlated Electrons
Abstract: Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.
Published: 2024

7. Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Author: Rosenberg, Eliott, Andersen, Trond, Samajdar, Rhine, Petukhov, Andre, Hoke, Jesse, Abanin, Dmitry, Bengtsson, Andreas, Drozdov, Ilya, Erickson, Catherine, Klimov, Paul, Mi, Xiao, Morvan, Alexis, Neeley, Matthew, Neill, Charles, Acharya, Rajeev, Allen, Richard, Anderson, Kyle, Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Bardin, Joseph, Bilmes, A., Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David, Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Campero, Juan, Chang, Hung-Shen, Chen, Zijun, Chiaro, Benjamin, Chik, Desmond, Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander, Curtin, Ben, Debroy, Dripto, Barba, Alexander Del Toro, Demura, Sean, Di Paolo, Agustin, Dunsworth, Andrew, Earle, Clint, Farhi, E., Fatemi, Reza, Ferreira, Vinicius, Flores, Leslie, Forati, Ebrahim, Fowler, Austin, Foxen, Brooks, Garcia, Gonzalo, Genois, Élie, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Gosula, Raja, Dau, Alejandro Grajales, Gross, Jonathan, Habegger, Steve, Hamilton, Michael, Hansen, Monica, Harrigan, Matthew, Harrington, Sean, Heu, Paula, Hill, Gordon, Hoffmann, Markus, Hong, Sabrina, Huang, Trent, Huff, Ashley, Huggins, William, Ioffe, Lev, Isakov, Sergei, Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Juhas, Pavol, Kafri, D., Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klots, Andrey, Korotkov, Alexander, Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim Ming, Laws, Lily, Lee, Joonho, Lee, Kenneth, Lensky, Yuri, Lester, Brian, Lill, Alexander, Liu, Wayne, Livingston, William P., Locharla, A., Mandrà, Salvatore, Martin, Orion, Martin, Steven, McClean, Jarrod, McEwen, Matthew, Meeks, Seneca, Miao, Kevin, Mieszala, Amanda, Montazeri, Shirin, Movassagh, Ramis, Mruczkiewicz, Wojciech, Nersisyan, Ani, Newman, Michael, Ng, Jiun How, Nguyen, Anthony, Nguyen, Murray, Niu, M., O'Brien, Thomas, Omonije, Seun, Opremcak, Alex, Potter, Rebecca, Pryadko, Leonid, Quintana, Chris, Rhodes, David, Rocque, Charles, Rubin, N., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin, Schurkus, Henry, Schuster, Christopher, Shearn, Michael, Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Sivak, Volodymyr, Skruzny, Jindra, Smith, Clarke, Somma, Rolando, Sterling, George, Strain, Doug, Szalay, Marco, Thor, Douglas, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Theodore, Woo, Bryan, Xing, Cheng, Yao, Jamie, Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Hartmut, Babbush, Ryan, Bacon, Dave, Boixo, Sergio, Hilton, Jeremy, Lucero, Erik, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Khemani, Vedika, Gopalakrishnan, Sarang, Prosen, Tomaž, and Roushan, Pedram
Subjects: Quantum Physics
Abstract: Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.
Published: 2023
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8. Measurement-induced entanglement and teleportation on a noisy quantum processor

Author: Hoke, Jesse C., Ippoliti, Matteo, Rosenberg, Eliott, Abanin, Dmitry, Acharya, Rajeev, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Bardin, Joseph C., Bengtsson, Andreas, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Chen, Zijun, Chiaro, Ben, Chik, Desmond, Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Dau, Alejandro Grajales, Debroy, Dripto M., Barba, Alexander Del Toro, Demura, Sean, Di Paolo, Augustin, Drozdov, Ilya K., Dunsworth, Andrew, Eppens, Daniel, Erickson, Catherine, Farhi, Edward, Fatemi, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Gosula, Raja, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heu, Paula, Hoffmann, Markus R., Hong, Sabrina, Huang, Trent, Huff, Ashley, Huggins, William J., Isakov, Sergei V., Iveland, Justin, Jeffrey, Evan, Jones, Cody, Juhas, Pavol, Kafri, Dvir, Kechedzhi, Kostyantyn, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Klots, Andrey R., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim-Ming, Laws, Lily, Lee, Joonho, Lee, Kenny W., Lensky, Yuri D., Lester, Brian J., Lill, Alexander T., Liu, Wayne, Locharla, Aditya, Martin, Orion, McClean, Jarrod R., McEwen, Matt, Miao, Kevin C., Mieszala, Amanda, Montazeri, Shirin, Morvan, Alexis, Movassagh, Ramis, Mruczkiewicz, Wojciech, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Newman, Michael, Ng, Jiun H., Nguyen, Anthony, Nguyen, Murray, Niu, Murphy Yuezhen, O'Brien, Tom E., Omonije, Seun, Opremcak, Alex, Petukhov, Andre, Potter, Rebecca, Pryadko, Leonid P., Quintana, Chris, Rocque, Charles, Rubin, Nicholas C., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vlad, Skruzny, Jindra, Smith, W. Clarke, Somma, Rolando D., Sterling, George, Strain, Douglas, Szalay, Marco, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Ted, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie., Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Harmut, Babbush, Ryan, Bacon, Dave, Boixo, Sergio, Hilton, Jeremy, Lucero, Erik, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Mi, Xiao, Khemani, Vedika, and Roushan, Pedram
Subjects: Quantum Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory
Abstract: Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.
Published: 2023
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9. Non-Abelian braiding of graph vertices in a superconducting processor

Author: Andersen, Trond I., Lensky, Yuri D., Kechedzhi, Kostyantyn, Drozdov, Ilya, Bengtsson, Andreas, Hong, Sabrina, Morvan, Alexis, Mi, Xiao, Opremcak, Alex, Acharya, Rajeev, Allen, Richard, Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Babbush, Ryan, Bacon, Dave, Bardin, Joseph C., Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Chen, Zijun, Chiaro, Ben, Chik, Desmond, Chou, Charina, Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Debroy, Dripto M., Barba, Alexander Del Toro, Demura, Sean, Dunsworth, Andrew, Eppens, Daniel, Erickson, Catherine, Faoro, Lara, Farhi, Edward, Fatemi, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Gosula, Raja, Dau, Alejandro Grajales, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heu, Paula, Hilton, Jeremy, Hoffmann, Markus R., Huang, Trent, Huff, Ashley, Huggins, William J., Ioffe, Lev B., Isakov, Sergei V., Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Juhas, Pavol, Kafri, Dvir, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Klots, Andrey R., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim-Ming, Laws, Lily, Lee, Joonho, Lee, Kenny, Lester, Brian J., Lill, Alexander, Liu, Wayne, Locharla, Aditya, Lucero, Erik, Malone, Fionn D., Martin, Orion, McClean, Jarrod R., McCourt, Trevor, McEwen, Matt, Miao, Kevin C., Mieszala, Amanda, Mohseni, Masoud, Montazeri, Shirin, Mount, Emily, Movassagh, Ramis, Mruczkiewicz, Wojciech, Naaman, Ofer, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Newman, Michael, Ng, Jiun How, Nguyen, Anthony, Nguyen, Murray, Niu, Murphy Yuezhen, O'Brien, Thomas E., Omonije, Seun, Petukhov, Andre, Potter, Rebecca, Pryadko, Leonid P., Quintana, Chris, Rocque, Charles, Rubin, Nicholas C., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Skruzny, Jindra, Smith, W. Clarke, Somma, Rolando, Sterling, George, Strain, Doug, Szalay, Marco, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Theodore, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Hartmut, Boixo, Sergio, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Kim, Eun-Ah, Aleiner, Igor, and Roushan, Pedram
Subjects: Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Other Condensed Matter
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.
Published: 2022

10. Suppressing quantum errors by scaling a surface code logical qubit

Author: Acharya, Rajeev, Aleiner, Igor, Allen, Richard, Andersen, Trond I., Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Babbush, Ryan, Bacon, Dave, Bardin, Joseph C., Basso, Joao, Bengtsson, Andreas, Boixo, Sergio, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Chen, Yu, Chen, Zijun, Chiaro, Ben, Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Debroy, Dripto M., Barba, Alexander Del Toro, Demura, Sean, Dunsworth, Andrew, Eppens, Daniel, Erickson, Catherine, Faoro, Lara, Farhi, Edward, Fatemi, Reza, Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Dau, Alejandro Grajales, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Harrigan, Matthew P., Harrington, Sean D., Higgott, Oscar, Hilton, Jeremy, Hoffmann, Markus, Hong, Sabrina, Huang, Trent, Huff, Ashley, Huggins, William J., Ioffe, Lev B., Isakov, Sergei V., Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Juhas, Pavol, Kafri, Dvir, Kechedzhi, Kostyantyn, Kelly, Julian, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Klots, Andrey R., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim-Ming, Laws, Lily, Lee, Joonho, Lee, Kenny, Lester, Brian J., Lill, Alexander, Liu, Wayne, Locharla, Aditya, Lucero, Erik, Malone, Fionn D., Marshall, Jeffrey, Martin, Orion, McClean, Jarrod R., Mccourt, Trevor, McEwen, Matt, Megrant, Anthony, Costa, Bernardo Meurer, Mi, Xiao, Miao, Kevin C., Mohseni, Masoud, Montazeri, Shirin, Morvan, Alexis, Mount, Emily, Mruczkiewicz, Wojciech, Naaman, Ofer, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Neven, Hartmut, Newman, Michael, Ng, Jiun How, Nguyen, Anthony, Nguyen, Murray, Niu, Murphy Yuezhen, O'Brien, Thomas E., Opremcak, Alex, Platt, John, Petukhov, Andre, Potter, Rebecca, Pryadko, Leonid P., Quintana, Chris, Roushan, Pedram, Rubin, Nicholas C., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shvarts, Vladimir, Skruzny, Jindra, Smelyanskiy, Vadim, Smith, W. Clarke, Sterling, George, Strain, Doug, Szalay, Marco, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Theodore, Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, and Zhu, Ningfeng
Subjects: Quantum Physics
Abstract: Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation., Comment: Main text: 6 pages, 4 figures. v2: Update author list, references, Fig. S12, Table IV
Published: 2022

11. Formation of robust bound states of interacting microwave photons

Author: Morvan, Alexis, Andersen, Trond I., Mi, Xiao, Neill, Charles, Petukhov, Andre, Kechedzhi, Kostyantyn, Abanin, Dmitry, Acharya, Rajeev, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Babbush, Ryan, Bacon, Dave, Bardin, Joseph C., Basso, Joao, Bengtsson, Andreas, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Chen, Zijun, Chiaro, Ben, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Debroy, Dripto M., Barba, Alexander Del Toro, Demura, Sean, Dunsworth, Andrew, Eppens, Daniel, Erickson, Catherine, Faoro, Lara, Farhi, Edward, Fatemi, Reza, Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Dau, Alejandro Grajales, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Harrigan, Matthew P., Harrington, Sean D., Hilton, Jeremy, Hoffmann, Markus, Hong, Sabrina, Huang, Trent, Huff, Ashley, Huggins, William J., Isakov, Sergei V., Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Juhas, Pavol, Kafri, Dvir, Khattar, Tanuj, Khezri, Mostafa, Kieferova, Marika, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Klots, Andrey R., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim-Ming, Laws, Lily, Lee, Joonho, Lee, Kenny, Lester, Brian J., Lill, Alexander, Liu, Wayne, Locharla, Aditya, Lucero, Erik, Malone, Fionn D., Martin, Orion, McClean, Jarrod R., McEwen, Matt, Costa, Bernardo Meurer, Miao, Kevin C., Mohseni, Masoud, Montazeri, Shirin, Mount, Emily, Mruczkiewicz, Wojciech, Naaman, Ofer, Neeley, Matthew, Nersisyan, Ani, Newman, Michael, Nguyen, Anthony, Nguyen, Murray, Niu, Murphy Yuezhen, O'Brien, Thomas E., Olenewa, Ricardo, Opremcak, Alex, Potter, Rebecca, Quintana, Chris, Rubin, Nicholas C., Saei, Negar, Sank, Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shvarts, Vladimir, Skruzny, Jindra, Smith, W. Clarke, Sterling, George, Strain, Doug, Su, Yuan, Szalay, Marco, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Theodore, Xing, Cheng, Yao, Z. Jamie, Yeh, Ping, Yoo, Juhwan, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Neven, Hartmut, Boixo, Sergio, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Aleiner, Igor, Ioffe, Lev B., and Roushan, Pedram
Subjects: Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Other Condensed Matter
Abstract: Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multi-particle bound states. In a ring of 24 superconducting qubits, we develop a high fidelity parameterizable fSim gate that we use to implement the periodic quantum circuit of the spin-1/2 XXZ model, an archetypal model of interaction. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons. We devise a phase sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the common wisdom that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit., Comment: 7 pages + 15 pages supplements
Published: 2022
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12. Overcoming leakage in quantum error correction

Author: Miao, Kevin C., McEwen, Matt, Atalaya, Juan, Kafri, Dvir, Pryadko, Leonid P., Bengtsson, Andreas, Opremcak, Alex, Satzinger, Kevin J., Chen, Zijun, Klimov, Paul V., Quintana, Chris, Acharya, Rajeev, Anderson, Kyle, Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Bardin, Joseph C., Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Campero, Juan, Chiaro, Ben, Collins, Roberto, Conner, Paul, Crook, Alexander L., Curtin, Ben, Debroy, Dripto M., Demura, Sean, Dunsworth, Andrew, Erickson, Catherine, Fatemi, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Garcia, Gonzalo, Giang, William, Gidney, Craig, Giustina, Marissa, Gosula, Raja, Dau, Alejandro Grajales, Gross, Jonathan A., Hamilton, Michael C., Harrington, Sean D., Heu, Paula, Hilton, Jeremy, Hoffmann, Markus R., Hong, Sabrina, Huang, Trent, Huff, Ashley, Iveland, Justin, Jeffrey, Evan, Jiang, Zhang, Jones, Cody, Kelly, Julian, Kim, Seon, Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Laws, Lily, Lee, Kenny, Lester, Brian J., Lill, Alexander T., Liu, Wayne, Locharla, Aditya, Lucero, Erik, Martin, Steven, Megrant, Anthony, Mi, Xiao, Montazeri, Shirin, Morvan, Alexis, Naaman, Ofer, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Newman, Michael, Ng, Jiun How, Nguyen, Anthony, Nguyen, Murray, Potter, Rebecca, Rocque, Charles, Roushan, Pedram, Sankaragomathi, Kannan, Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vladimir, Skruzny, Jindra, Smith, W. Clarke, Sterling, George, Szalay, Marco, Thor, Douglas, Torres, Alfredo, White, Theodore, Woo, Bryan W. K., Yao, Z. Jamie, Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Hartmut, Smelyanskiy, Vadim, Petukhov, Andre, Korotkov, Alexander N., Sank, Daniel, and Chen, Yu
Published: 2023
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13. Recent developments in the PySCF program package

Author: Sun, Qiming, Zhang, Xing, Banerjee, Samragni, Bao, Peng, Barbry, Marc, Blunt, Nick S., Bogdanov, Nikolay A., Booth, George H., Chen, Jia, Cui, Zhi-Hao, Eriksen, Janus Juul, Gao, Yang, Guo, Sheng, Hermann, Jan, Hermes, Matthew R., Koh, Kevin, Koval, Peter, Lehtola, Susi, Li, Zhendong, Liu, Junzi, Mardirossian, Narbe, McClain, James D., Motta, Mario, Mussard, Bastien, Pham, Hung Q., Pulkin, Artem, Purwanto, Wirawan, Robinson, Paul J., Ronca, Enrico, Sayfutyarova, Elvira, Scheurer, Maximilian, Schurkus, Henry F., Smith, James E. T., Sun, Chong, Sun, Shi-Ning, Upadhyay, Shiv, Wagner, Lucas K., Wang, Xiao, White, Alec, Whitfield, James Daniel, Williamson, Mark J., Wouters, Sebastian, Yang, Jun, Yu, Jason M., Zhu, Tianyu, Berkelbach, Timothy C., Sharma, Sandeep, Sokolov, Alexander, and Chan, Garnet Kin-Lic
Subjects: Physics - Chemical Physics, Physics - Computational Physics
Abstract: PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.
Published: 2020
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14. Theoretical Prediction of Magnetic Exchange Coupling Constants from Broken-Symmetry Coupled Cluster Calculations

Author: Schurkus, Henry F., Chen, Dian-Teng, Cheng, Hai-Ping, Chan, Garnet Kin-Lic, and Stanton, John F.
Subjects: Physics - Chemical Physics
Abstract: Exchange coupling constants ($J$) are fundamental to the understanding of spin spectra of magnetic systems. Here we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. $J$ values calculated from CC in this fashion converge smoothly towards the FCI result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary EOM-CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.
Published: 2020
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15. Exploring the magnetic properties of the largest single molecule magnets

Author: Schurkus, Henry F., Chen, Dianteng, O'Rourke, Matthew J., Cheng, Hai-Ping, and Chan, Garnet K. -L.
Subjects: Physics - Chemical Physics
Abstract: The giant $\{ \mathrm{Mn}_{70} \}$ and $\{ \mathrm{Mn}_{84} \}$ wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled $\{ \mathrm{Mn}_{7} \}$ subunits carrying an effective $S=2$ spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest energy excitations arising from Heisenberg-ring-like excitations of the $\{ \mathrm{Mn}_{7} \}$ subunits around the wheel, at energies consistent with the observed temperature dependence of the magnetic susceptibility. We further suggest an important role for weak longer-range couplings in selecting the precise spin ground-state of the $\mathrm{Mn}$ wheels out of the nearly degenerate ground-state band., Comment: 7 pages, 8 figures. HFS and DTC contributed equally
Published: 2020

16. Quantum information phases in space-time: measurement-induced entanglement and teleportation on a noisy quantum processor

Author: Hoke, Jesse, primary, Ippoliti, Matteo, additional, Abanin, Dmitry, additional, Acharya, Rajeev, additional, Ansmann, Markus, additional, Arute, Frank, additional, Arya, Kunal, additional, Asfaw, Abraham, additional, Atalaya, Juan, additional, Babbush, Ryan, additional, Bardin, Joseph, additional, Bengtsson, Andreas, additional, Bortoli, Gina, additional, Bourassa, Alexandre, additional, Bovaird, Jenna, additional, Brill, Leon, additional, Broughton, Michael, additional, Buckley, Bob, additional, Buell, David, additional, Burger, Tim, additional, Burkett, Brian, additional, Bushnell, Nicholas, additional, Chen, Zijun, additional, Chiaro, Ben, additional, Chik, Desmond, additional, Chou, Charina, additional, Cogan, Josh, additional, Collins, Roberto, additional, Conner, Paul, additional, Courtney, William, additional, Crook, Alexander, additional, Curtin, Ben, additional, Dau, Alejandro Grajales, additional, Debroy, Dripto, additional, Barba, Alexander Del Toro, additional, Demura, Sean, additional, Paolo, Augustin Di, additional, Drozdov, Ilya, additional, Dunsworth, Andrew, additional, Eppens, Daniel, additional, Erickson, Catherine, additional, Faoro, Lara, additional, Farhi, Edward, additional, Fatemi, Reza, additional, Ferreira, Vinicius, additional, Burgos, Leslie Flores, additional, Forati, Ebrahim, additional, Fowler, Austin, additional, Foxen, Brooks, additional, Giang, William, additional, Gidney, Craig, additional, Gilboa, Dar, additional, Giustina, Marissa, additional, Gosula, Raja, additional, Gross, Jonathan, additional, Habegger, Steve, additional, Hamilton, Michael, additional, Hansen, Monica, additional, Harrigan, Matthew, additional, Harrington, Sean, additional, Heu, Paula, additional, Hoffmann, Markus, additional, Hong, Sabrina, additional, Huang, Trent, additional, Huff, Ashley, additional, Huggins, William, additional, Isakov, Sergei, additional, Iveland, Justin, additional, Jeffrey, E., additional, Jones, Cody, additional, Juhas, Pavol, additional, Kafri, Dvir, additional, Kechedzhi, Kostyantyn, additional, Khattar, Tanuj, additional, Khezri, Mostafa, additional, Kieferova, Marika, additional, Kim, Seon, additional, Kitaev, Alexei, additional, Klimov, Paul, additional, Klots, Andrey, additional, Korotkov, Alexander, additional, Kostritsa, Fedor, additional, Kreikebaum, John Mark, additional, Landhuis, David, additional, Laptev, Pavel, additional, Lau, Kim-Ming, additional, Laws, Lily, additional, Lee, Joonho, additional, Lee, Kenny, additional, Lensky, Yuri, additional, Lester, Brian, additional, Lill, Alexander, additional, Liu, Wayne, additional, Locharla, Aditya, additional, Malone, Fionn, additional, Martin, Orion, additional, McClean, Jarrod, additional, McEwen, Matt, additional, Miao, Kevin, additional, Mieszala, Amanda, additional, Montazeri, Shirin, additional, Morvan, Alexis, additional, Movassagh, Ramis, additional, Mruczkiewicz, Wojciech, additional, Neeley, Matthew, additional, Neill, Charles, additional, Nersisyan, Ani, additional, Newman, Michael, additional, Ng, Jiun How, additional, Nguyen, Anthony, additional, Nguyen, Murray, additional, Niu, Murphy, additional, O'Brien, Thomas, additional, Omonije, Seun, additional, Opremcak, Alex, additional, Petukhov, Andre, additional, Potter, Rebecca, additional, Pryadko, Leonid, additional, Quintana, Chris, additional, Rocque, Charles, additional, Rubin, Nicholas, additional, Saei, Negar, additional, Sank, Daniel, additional, Sankaragomathi, Kannan, additional, Satzinger, Kevin, additional, Schurkus, Henry, additional, Schuster, Christopher, additional, Shearn, Michael, additional, Shorter, Aaron, additional, Shutty, Noah, additional, Vladimir, Shvarts, additional, Skruzny, Jindra, additional, Smith, W., additional, Somma, Rolando, additional, Sterling, George, additional, Strain, Doug, additional, Szalay, Marco, additional, Torres, Alfredo, additional, Vidal, Guifre, additional, Villalonga, Benjamin, additional, Heidweiller, Catherine Vollgraff, additional, White, Theodore, additional, Woo, Bryan, additional, Xing, Cheng, additional, Yao, Z. Jamie, additional, Yeh, Ping, additional, Yoo, Juhwan, additional, Young, Grayson, additional, Zalcman, Adam, additional, Zhang, Yaxing, additional, Zhu, Ningfeng, additional, Zobrist, Nicholas, additional, Neven, Hartmut, additional, Bacon, Dave, additional, Boixo, Sergio, additional, Hilton, Jeremy, additional, Lucero, Erik, additional, Megrant, Anthony, additional, Kelly, Julian, additional, Chen, Yu, additional, Smelyanskiy, Vadim, additional, Mi, Xiao, additional, Khemani, Vedika, additional, and Roushan, Pedram, additional
Published: 2023
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17. Quantum information phases in space-time: measurement-induced entanglement and teleportation on a noisy quantum processor

Author: Hoke, Jesse C., Ippoliti, Matteo, Abanin, Dmitry, Acharya, Rajeev, Ansmann, Markus, Arute, Frank, Arya, Kunal, Asfaw, Abraham, Atalaya, Juan, Bardin, Joseph C., Bengtsson, Andreas, Bortoli, Gina, Bourassa, Alexandre, Bovaird, Jenna, Brill, Leon, Broughton, Michael, Buckley, Bob B., Buell, David A., Burger, Tim, Burkett, Brian, Bushnell, Nicholas, Chen, Zijun, Chiaro, Ben, Chik, Desmond, Chou, Charina, Cogan, Josh, Collins, Roberto, Conner, Paul, Courtney, William, Crook, Alexander L., Curtin, Ben, Dau, Alejandro Grajales, Debroy, Dripto M., Barba, Alexander Del Toro, Demura, Sean, Di Paolo, Augustin, Drozdov, Ilya K., Dunsworth, Andrew, Eppens, Daniel, Erickson, Catherine, Faoro, Lara, Farhi, Edward, Fatem, Reza, Ferreira, Vinicius S., Burgos, Leslie Flores, Forati, Ebrahim, Fowler, Austin G., Foxen, Brooks, Giang, William, Gidney, Craig, Gilboa, Dar, Giustina, Marissa, Gosula, Raja, Gross, Jonathan A., Habegger, Steve, Hamilton, Michael C., Hansen, Monica, Harrigan, Matthew P., Harrington, Sean D., Heu, Paula, Hoffmann, Markus R., Hong, Sabrina, Huang, Trent, Huff, Ashley, Huggins, William J., Isakov, Sergei V., Iveland, Justin, Jeffr, Evan, Jones, Cody, Juhas, Pavol, Kafri, Dvir, Kechedzhi, Kostyantyn, Khattar, Tanuj, Khezri, Mostafa, Kieferová, Mária, Kim, Seon, Kitaev, Alexei, Klimov, Paul V., Klots, Andrey R., Korotkov, Alexander N., Kostritsa, Fedor, Kreikebaum, John Mark, Landhuis, David, Laptev, Pavel, Lau, Kim-Ming, Laws, Lily, Lee, Joonho, Lee, Kenny W., Lensky, Yuri D., Lester, Brian J., Lill, Alexander T., Liu, Wayne, Locharla, Aditya, Malone, Fionn D., Martin, Orion, McClean, Jarrod R., McCourt, Trevor, McEwen, Matt, Miao, Kevin C., Mieszala, Amanda, Montazeri, Shirin, Morvan, Alexis, Movassagh, Ramis, Mruczkiewicz, Wojciech, Neeley, Matthew, Neill, Charles, Nersisyan, Ani, Newman, Michael, Ng, Jiun H., Nguyen, Anthony, Nguyen, Murray, Niu, Murphy Yuezhen, O'Brien, Tom E., Omonije, Seun, Opremcak, Alex, Petukhov, Andre, Potter, Rebecca, Pryadko, Leonid P., Quintana, Chris, Rocque, Charles, Rubin, Nicholas C., Sank, Negar Saei Daniel, Sankaragomathi, Kannan, Satzinger, Kevin J., Schurkus, Henry F., Schuster, Christopher, Shearn, Michael J., Shorter, Aaron, Shutty, Noah, Shvarts, Vlad, Skruzny, Jindra, Smith, W. Clarke, Sterling, Rolando D. Somma George, Strain, Douglas, Szalay, Marco, Torres, Alfredo, Vidal, Guifre, Villalonga, Benjamin, Heidweiller, Catherine Vollgraff, White, Ted, Woo, Bryan W. K., Xing, Cheng, Yao, Z. Jamie., Yeh, Ping, Yoo, Juhwan, Young, Grayson, Zalcman, Adam, Zhang, Yaxing, Zhu, Ningfeng, Zobrist, Nicholas, Neven, Harmut, Babbush, Ryan, Bacon, Dave, Boixo, Sergio, Hilton, Jeremy, Lucero, Erik, Megrant, Anthony, Kelly, Julian, Chen, Yu, Smelyanskiy, Vadim, Mi, Xiao, Khemani, Vedika, and Roushan, Pedram
Subjects: High Energy Physics - Theory, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), High Energy Physics - Theory (hep-th), FOS: Physical sciences, Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics
Abstract: Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.
Published: 2023

18. Purification-based quantum error mitigation of pair-correlated electron simulations

Author: O'Brien, Thomas, primary, Anselmetti, Gian-Luca, additional, Gkritsis, Fotios, additional, Elfving, Vincent, additional, Polla, Stefano, additional, Huggins, William, additional, Oumarou, Oumarou, additional, Kechedzhi, Kostyantyn, additional, Abanin, Dmitry, additional, Acharya, Rajeev, additional, Aleiner, Igor, additional, Allen, Richard, additional, Andersen, Trond, additional, Anderson, Kyle, additional, Ansmann, Markus, additional, Arute, Frank, additional, Arya, Kunal, additional, Asfaw, Abraham, additional, Atalaya, Juan, additional, Bacon, Dave, additional, Bardin, Joseph, additional, Bengtsson, Andreas, additional, Boixo, Sergio, additional, Bortoli, Gina, additional, Bourassa, Alexandre, additional, Bovaird, Jenna, additional, Brill, Leon, additional, Broughton, Michael, additional, Buckley, Bob, additional, Buell, David, additional, Burger, Tim, additional, Burkett, Brian, additional, Bushnell, Nicholas, additional, Campero, Juan, additional, Chen, Yu, additional, Chen, Zijun, additional, Chiaro, Ben, additional, Chik, Desmond, additional, Cogan, Josh, additional, Collins, Roberto, additional, Conner, Paul, additional, Courtney, William, additional, Crook, Alexander, additional, Curtin, Ben, additional, Debroy, Dripto, additional, Barba, Alexander Del Toro, additional, Demura, Sean, additional, Drozdov, Ilya, additional, Dunsworth, Andrew, additional, Eppens, Daniel, additional, Erickson, Catherine, additional, Faoro, Lara, additional, Farhi, Edward, additional, Fatemi, Reza, additional, Ferreira, Vinicius, additional, Burgos, Leslie Flores, additional, Forati, Ebrahim, additional, Fowler, Austin, additional, Foxen, Brooks, additional, Giang, William, additional, Gidney, Craig, additional, Gilboa, Dar, additional, Giustina, Marissa, additional, Gosula, Raja, additional, Dau, Alejandro Grajales, additional, Gross, Jonathan, additional, Habegger, Steve, additional, Hamilton, Michael, additional, Hansen, Monica, additional, Harrigan, Matthew, additional, Harrington, Sean, additional, Heu, Paula, additional, Hilton, Jeremy, additional, Hoffmann, Markus, additional, Hong, Sabrina, additional, Huang, Trent, additional, Huff, Ashley, additional, Ioffe, L. B., additional, Isakov, Sergei, additional, Iveland, Justin, additional, Jeffrey, E., additional, Jiang, Zhang, additional, Jones, Cody, additional, Juhas, Pavol, additional, Kafri, Dvir, additional, Kelly, Julian, additional, Khattar, Tanuj, additional, Khezri, Mostafa, additional, Kieferova, Marika, additional, Kim, Seon, additional, Klimov, Paul, additional, Klots, Andrey, additional, Korotkov, Alexander, additional, Kostritsa, Fedor, additional, Kreikebaum, John Mark, additional, Landhuis, David, additional, Laptev, Pavel, additional, Lau, Kim-Ming, additional, Laws, Lily, additional, Lee, Joonho, additional, Lee, Kenny, additional, Lester, Brian, additional, Lill, Alexander, additional, Liu, Wayne, additional, Livingston, William, additional, Locharla, Aditya, additional, Lucero, Erik, additional, Malone, Fionn, additional, Mandra, Salvatore, additional, Martin, Orion, additional, Martin, Steven, additional, McClean, Jarrod, additional, McCourt, Trevor, additional, McEwen, Matthew, additional, Megrant, Anthony, additional, Mi, Xiao, additional, Miao, Kevin, additional, Mieszala, Amanda, additional, Mohseni, Masoud, additional, Montazeri, Shirin, additional, Morvan, Alexis, additional, Movassagh, Ramis, additional, Mruczkiewicz, Wojciech, additional, Naaman, Ofer, additional, Neeley, Matthew, additional, Neill, Charles, additional, Nersisyan, Ani, additional, Neven, Hartmut, additional, Newman, Michael, additional, Ng, Jiun How, additional, Nguyen, Anthony, additional, Nguyen, Murray, additional, Niu, Murphy, additional, Omonije, Seun, additional, Opremcak, Alex, additional, Petukhov, Andre, additional, Potter, Rebecca, additional, Pryadko, Leonid, additional, Quintana, Chris, additional, Rocque, Charles, additional, Roushan, Pedram, additional, Saei, Negar, additional, Sank, Daniel, additional, Sankaragomathi, Kannan, additional, Satzinger, Kevin, additional, Schurkus, Henry, additional, Shearn, Michael, additional, Shorter, Aaron, additional, Shutty, Noah, additional, Vladimir, Shvarts, additional, Skruzny, Jindra, additional, Smelyanskiy, Vadim, additional, Smith, W. Clarke, additional, Somma, Rolando, additional, Sterling, George, additional, Strain, Doug, additional, Szalay, Marco, additional, Thor, Douglas, additional, Torres, Alfredo, additional, Vidal, Guifre, additional, Villalonga, Benjamin, additional, Heidweiller, Catherine Vollgraff, additional, White, Theodore, additional, Woo, Bryan, additional, Xing, Cheng, additional, Yao, Z. Jamie, additional, Yeh, Ping, additional, Yoo, Juhwan, additional, Young, Grayson, additional, Zalcman, Adam, additional, Zhang, Yaxing, additional, Zhu, Ningfeng, additional, Zobrist, Nicholas, additional, Gogolin, Christian, additional, Babbush, Ryan, additional, and Rubin, Nicholas, additional
Published: 2022
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19. Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism.

Author: Beuerle, Matthias, Graf, Daniel, Schurkus, Henry F., and Ochsenfeld, Christian
Subjects: COMPUTATIONAL chemistry, DISPERSION (Atmospheric chemistry), HARTREE-Fock approximation, PHASE transitions, LAPLACE transformation, POLARIZATION (Electrochemistry)
Abstract: We present efficient methods to calculate beyond random phase approximation (RPA) correlation energies for molecular systems with up to 500 atoms. To reduce the computational cost, we employ the resolution-of-the-identity and a double-Laplace transform of the non-interacting polarization propagator in conjunction with an atomic orbital formalism. Further improvements are achieved using integral screening and the introduction of Cholesky decomposed densities. Our methods are applicable to the dielectric matrix formalism of RPA including second-order screened exchange (RPA-SOSEX), the RPA electron-hole time-dependent Hartree-Fock (RPA-eh-TDHF) approximation, and RPA renormalized perturbation theory using an approximate exchange kernel (RPA-AXK). We give an application of our methodology by presenting RPA-SOSEX benchmark results for the L7 test set of large, dispersion dominated molecules, yielding a mean absolute error below 1 kcal/mol. The present work enables calculating beyond RPA correlation energies for significantly larger molecules than possible to date, thereby extending the applicability of these methods to a wider range of chemical systems. [ABSTRACT FROM AUTHOR]
Published: 2018
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20. Recent developments in the PySCF program package

Author: Sun, Qiming, primary, Zhang, Xing, additional, Banerjee, Samragni, additional, Bao, Peng, additional, Barbry, Marc, additional, Blunt, Nick S., additional, Bogdanov, Nikolay A., additional, Booth, George H., additional, Chen, Jia, additional, Cui, Zhi-Hao, additional, Eriksen, Janus J., additional, Gao, Yang, additional, Guo, Sheng, additional, Hermann, Jan, additional, Hermes, Matthew R., additional, Koh, Kevin, additional, Koval, Peter, additional, Lehtola, Susi, additional, Li, Zhendong, additional, Liu, Junzi, additional, Mardirossian, Narbe, additional, McClain, James D., additional, Motta, Mario, additional, Mussard, Bastien, additional, Pham, Hung Q., additional, Pulkin, Artem, additional, Purwanto, Wirawan, additional, Robinson, Paul J., additional, Ronca, Enrico, additional, Sayfutyarova, Elvira R., additional, Scheurer, Maximilian, additional, Schurkus, Henry F., additional, Smith, James E. T., additional, Sun, Chong, additional, Sun, Shi-Ning, additional, Upadhyay, Shiv, additional, Wagner, Lucas K., additional, Wang, Xiao, additional, White, Alec, additional, Whitfield, James Daniel, additional, Williamson, Mark J., additional, Wouters, Sebastian, additional, Yang, Jun, additional, Yu, Jason M., additional, Zhu, Tianyu, additional, Berkelbach, Timothy C., additional, Sharma, Sandeep, additional, Sokolov, Alexander Yu., additional, and Chan, Garnet Kin-Lic, additional
Published: 2020
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21. Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations

Author: Schurkus, Henry, primary, Chen, Dian-Teng, additional, Cheng, Hai-Ping, additional, Chan, Garnet, additional, and Stanton, John, additional
Published: 2020
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22. Exploring the Magnetic Properties of the Largest Single-Molecule Magnets

Author: Schurkus, Henry F., primary, Chen, Dianteng, additional, O’Rourke, Matthew J., additional, Cheng, Hai-Ping, additional, and Chan, Garnet Kin-Lic, additional
Published: 2020
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23. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation.

Author: Schurkus, Henry F. and Ochsenfeld, Christian
Subjects: *ATOMIC orbitals, *MATHEMATICAL reformulation, *LAPLACE transformation, *APPROXIMATION theory, *PERSONAL computers
Abstract: An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions. [ABSTRACT FROM AUTHOR]
Published: 2016
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24. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method

Author: Graf, Daniel, primary, Beuerle, Matthias, additional, Schurkus, Henry F., additional, Luenser, Arne, additional, Savasci, Gökcen, additional, and Ochsenfeld, Christian, additional
Published: 2018
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25. Highly Accurate Random Phase Approximation Methods With Linear Time Complexity

Author: Schurkus, Henry F.
Subjects: FOS: Chemical sciences
Abstract: One of the key challenges of electronic structure theory is to find formulations to compute electronic ground-state energies with high accuracy while being applicable to a wide range of chemical problems. For systems beyond the few atom scale often computations achieving higher accuracies than the so called double-hybrid density functional approximations become prohibitively expensive. Here, the random phase approximation, which is known to yield such higher accuracy results has been developed from a theory applicable only to molecules on the tens of atoms scale into a highly accurate and widely applicable theory. To this end, a mathematical understanding has been developed that, without changing the computational complexity, allows to eliminate the error introduced by the resolution-of-the-identity approximation which had been introduced in the previous formulation. Furthermore, in this work a new formulation of the random phase approximation for molecules has been presented which achieves linear-scaling of compute time with molecular size - thereby expanding the realm of molecules that can be treated on this level of theory to up to a thousand atoms on a simple desktop computer. Finally, the theory has been matured to allow for use of even extensive basis sets without drastically increasing runtimes. Overall, the presented theory is at least as accurate and even faster than the original formulation for all molecules for which compute time is significant and opens new possibilities for the highly accurate description of large quantum chemical systems.
Published: 2017
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26. Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions

Author: Schurkus, Henry F., primary, Luenser, Arne, additional, and Ochsenfeld, Christian, additional
Published: 2017
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27. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric

Author: Luenser, Arne, primary, Schurkus, Henry F., additional, and Ochsenfeld, Christian, additional
Published: 2017
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27 results on '"Schurkus, Henry"'

1. Demonstrating dynamic surface codes

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

3. Observation of disorder-free localization and efficient disorder averaging on a quantum processor

4. Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

5. Quantum error correction below the surface code threshold

6. Thermalization and Criticality on an Analog-Digital Quantum Simulator

7. Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

8. Measurement-induced entanglement and teleportation on a noisy quantum processor

9. Non-Abelian braiding of graph vertices in a superconducting processor

10. Suppressing quantum errors by scaling a surface code logical qubit

11. Formation of robust bound states of interacting microwave photons

12. Overcoming leakage in quantum error correction

13. Recent developments in the PySCF program package

14. Theoretical Prediction of Magnetic Exchange Coupling Constants from Broken-Symmetry Coupled Cluster Calculations

15. Exploring the magnetic properties of the largest single molecule magnets

16. Quantum information phases in space-time: measurement-induced entanglement and teleportation on a noisy quantum processor

17. Quantum information phases in space-time: measurement-induced entanglement and teleportation on a noisy quantum processor

18. Purification-based quantum error mitigation of pair-correlated electron simulations

19. Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism.

20. Recent developments in the PySCF program package

21. Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations

22. Exploring the Magnetic Properties of the Largest Single-Molecule Magnets

23. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation.

24. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method

25. Highly Accurate Random Phase Approximation Methods With Linear Time Complexity

26. Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions

27. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric

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27 results on '"Schurkus, Henry"'

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