Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Yu-An Chen, Ben Chiaro, Roberto Collins, Stephen J. Cotton, William Courtney, Sean Demura, Alan Derk, Andrew Dunsworth, Daniel Eppens, Thomas Eckl, Catherine Erickson, Edward Farhi, Austin Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Rob Graff, Jonathan A. Gross, Steve Habegger, Matthew P. Harrigan, Alan Ho, Sabrina Hong, Trent Huang, William Huggins, Lev B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Seon Kim, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Erik Lucero, Michael Marthaler, Orion Martin, John M. Martinis, Anika Marusczyk, Sam McArdle, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Anthony Megrant, Carlos Mejuto-Zaera, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Hartmut Neven, Michael Newman, Murphy Yuezhen Niu, Thomas E. O'Brien, Eric Ostby, Bálint Pató, Andre Petukhov, Harald Putterman, Chris Quintana, Jan-Michael Reiner, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Doug Strain, Kevin J. Sung, Peter Schmitteckert, Marco Szalay, Norm M. Tubman, Amit Vainsencher, Theodore White, Nicolas Vogt, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Sebastian Zanker

Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.

Readout of a quantum processor with high dynamic range Josephson parametric amplifiers

T. C. White, Alex Opremcak, George Sterling, Alexander Korotkov, Daniel Sank, Rajeev Acharya, Markus Ansmann, Frank Arute, Kunal Arya, Joseph C. Bardin, Andreas Bengtsson, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Zijun Chen, Ben Chiaro, Josh Cogan, Roberto Collins, Alexander L. Crook, Ben Curtin, Sean Demura, Andrew Dunsworth, Catherine Erickson, Reza Fatemi, Leslie Flores-Burgos, Ebrahim Forati, Brooks Foxen, William Giang, Marissa Giustina, Alejandro Grajales Dau, Michael C. Hamilton, Sean D. Harrington, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, Justin Iveland, Evan Jeffrey, Márika Kieferová, Seon Kim, Paul V. Klimov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Lily Laws, Kenny Lee, Brian J. Lester, Alexander Lill, Wayne Liu, Aditya Locharla, Erik Lucero, Trevor McCourt, Matt McEwen, Xiao Mi, Kevin C. Miao, Shirin Montazeri, Alexis Morvan, Matthew Neeley, Charles Neill, Ani Nersisyan, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Rebecca Potter, Chris Quintana, Pedram Roushan, Kannan Sankaragomathi, Kevin J. Satzinger, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Vladimir Shvarts, Jindra Skruzny, W. Clarke Smith, Marco Szalay, Alfredo Torres, Bryan Woo, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Ningfeng Zhu, Nicholas Zobrist, Yu Chen, Anthony Megrant, Julian Kelly, Ofer Naaman

We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 $Ω$ environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs.

Fast Scalable State Measurement with Superconducting Qubits

Daniel Sank, Evan Jeffrey, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O'Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, J. M. Martinis

Progress in superconducting qubit experiments with greater numbers of qubits or advanced techniques such as feedback requires faster and more accurate state measurement. We have designed a multiplexed measurement system with a bandpass filter that allows fast measurement without increasing environmental damping of the qubits. We use this to demonstrate simultaneous measurement of four qubits on a single superconducting integrated circuit, the fastest of which can be measured to 99.8% accuracy in 140ns. This accuracy and speed is suitable for advanced multi-qubit experiments including surface code error correction.

Surface spin fluctuations probed with flux noise and coherence in Josephson phase qubits

Daniel Sank, R. Barends, Radoslaw C. Bialczak, Yu Chen, J. Kelly, M. Lenander, E. Lucero, Matteo Mariantoni, M. Neeley, P. J. J. O'Malley, A. Vaisencher, H. Wang, J. Wenner, T. C. White, T. Yamamoto, Yi Yin, A. N. Cleland, John M. Martinis

We measure the dependence of qubit phase coherence and surface spin induced flux noise on inductor loop geometry. While wider inductor traces change neither the flux noise power spectrum nor the qubit dephasing time, increased inductance leads to a simultaneous increase in both. Using our protocol for measuring low frequency flux noise, we make a direct comparison between the flux noise spectrum and qubit phase decay, finding agreement within 10% of theory. The dependence of the measured flux noise on inductor geometry is consistent with a noise source correlation length between 6 and 400 um.

Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation

Daniel Sank, Zijun Chen, Mostafa Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, T. White, Alexander N. Korotkov, John M. Martinis

Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found that such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace, and that they show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian that are typically ignored by the rotating wave approximation. We find that the most important of these terms comes from an unexpected broken symmetry in the qubit potential. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.

System Characterization of Dispersive Readout in Superconducting Qubits

Daniel Sank, Alex Opremcak, Andreas Bengtsson, Mostafa Khezri, Zijun Chen, Ofer Naaman, Alexander Korotkov

Designing quantum systems with the measurement speed and accuracy needed for quantum error correction using superconducting qubits requires iterative design and test informed by accurate models and characterization tools. We introduce a single protocol, with few prerequisite calibrations, which measures the dispersive shift, resonator linewidth, and drive power used in the dispersive readout of superconducting qubits. We find that the resonator linewidth is poorly controlled with a factor of 2 between the maximum and minimum measured values, and is likely to require focused attention in future quantum error correction experiments. We also introduce a protocol for measuring the readout system efficiency using the same power levels as are used in typical qubit readout, and without the need to measure the qubit coherence. We routinely run these protocols on chips with tens of qubits, driven by automation software with little human interaction. Using the extracted system parameters, we find that a model based on those parameters predicts the readout signal to noise ratio to within 10% over a device with 54 qubits.

Balanced Coupling in Electromagnetic Circuits

Daniel Sank, Mostafa Khezri, Sergei Isakov, Juan Atalaya

The rotating wave approximation (RWA) is ubiquitous in the analysis of driven and coupled resonators. However, the limitations of the RWA seem to be poorly understood and in some cases the RWA disposes of essential physics. We investigate the RWA in the context of electrical resonant circuits. Using a classical Hamiltonian approach, we find that by balancing electrical and magnetic components of the resonator drive or resonator-resonator coupling, the RWA can be made exact. This type of balance, in which the RWA is exact, has applications in superconducting qubits where it suppresses nutation normally associated with strong Rabi driving. In the context of dispersive readout, balancing the qubit-resonator coupling changes the qubit leakage induced by the resonator drive (MIST), but does not remove it in the case of the transmon qubit.

Overcoming leakage in scalable quantum error correction

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

Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC). In a QEC circuit, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of logical error with scale, challenging the feasibility of QEC as a path towards fault-tolerant quantum computation. Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 \times 10^{-3}$ throughout the entire device. The leakage removal process itself efficiently returns leakage population back to the computational basis, and adding it to a code circuit prevents leakage from inducing correlated error across cycles, restoring a fundamental assumption of QEC. With this demonstration that leakage can be contained, we resolve a key challenge for practical QEC at scale.

Suppressing quantum errors by scaling a surface code logical qubit

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

Measurement-Induced State transitions in Inductively-Shunted Transmons

Nicholas Zobrist, John Mark Kreikebaum, Mostafa Khezri, Sergei V. Isakov, Brian J. Lester, Yaxing Zhang, Agustin Di Paolo, Daniel Sank, W. Clarke Smith

Fast and high-fidelity qubit measurement plays a key role in quantum error correction. In superconducting qubits, measurement is typically performed using a resonant microwave drive on a readout resonator dispersively coupled to the qubit. Shorter measurement times require larger numbers of photons populating the readout resonator, which ultimately leads to undesired measurementinduced state transitions (MIST) of the qubit. MIST can be particularly problematic because these transitions often leave the qubit in a high energy state, and the MIST locations in readout parameter space drift as a function of qubit offset charge. In transmon qubits, these drifts have been avoided using very large qubit-resonator detunings or dedicated offset charge biases. In this work, we take an alternative approach and add an inductive shunt to the transmon to eliminate the offset charge dependence and stabilize the MIST. We experimentally characterize MIST in several different inductively-shunted transmons, in agreement with quantum and semiclassical models for MIST. These results extend to other inductively-shunted qubits.

Information Scrambling in Computationally Complex Quantum Circuits

Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandra, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Julian Kelly, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Anthony Megrant, Kevin C. Miao, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Michael Newman, Murphy Yuezhen Niu, Thomas E. O'Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas Redd, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, Igor Aleiner, Kostyantyn Kechedzhi, Vadim Smelyanskiy, Yu Chen

Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish the two mechanisms associated with quantum scrambling, operator spreading and operator entanglement, and experimentally observe their respective signatures. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

Fabrication and Characterization of Aluminum Airbridges for Superconducting Microwave Circuits

Zijun Chen, Anthony Megrant, Julian Kelly, Rami Barends, Joerg Bochmann, Yu Chen, Ben Chiaro, Andrew Dunsworth, Evan Jeffrey, Joshua Mutus, Peter O'Malley, Charles Neill, Pedram Roushan, Daniel Sank, Amit Vainsencher, James Wenner, Theodore White, Andrew Cleland, John Martinis

Superconducting microwave circuits based on coplanar waveguides (CPW) are susceptible to parasitic slotline modes which can lead to loss and decoherence. We motivate the use of superconducting airbridges as a reliable method for preventing the propagation of these modes. We describe the fabrication of these airbridges on superconducting resonators, which we use to measure the loss due to placing airbridges over CPW lines. We find that the additional loss at single photon levels is small, and decreases at higher drive powers.

Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits

Radoslaw C. Bialczak, Markus Ansmann, Max Hofheinz, Erik Lucero, Matthew Neeley, Aaron O'Connell, Daniel Sank, Haohua Wang, James Wenner, Matthias Steffen, Andrew Cleland, John Martinis

Quantum logic gates must perform properly when operating on their standard input basis states, as well as when operating on complex superpositions of these states. Experiments using superconducting qubits have validated the truth table for particular implementations of e.g. the controlled-NOT gate [1,2], but have not fully characterized gate operation for arbitrary superpositions of input states. Here we demonstrate the use of quantum process tomography (QPT) [3,4] to fully characterize the performance of a universal entangling gate between two superconducting quantum bits. Process tomography permits complete gate analysis, but requires precise preparation of arbitrary input states, control over the subsequent qubit interaction, and simultaneous single-shot measurement of the output states. We use QPT to measure the fidelity of the entangling gate and to quantify the decoherence mechanisms affecting the gate performance. In addition to demonstrating a promising fidelity, our entangling gate has a on/off ratio of 300, a level of adjustable coupling that will become a requirement for future high-fidelity devices. This is the first solid-state demonstration of QPT in a two-qubit system, as solid-state process tomography has previously only been demonstrated with single qubits [5,6].

Model-based Optimization of Superconducting Qubit Readout

Andreas Bengtsson, Alex Opremcak, Mostafa Khezri, Daniel Sank, Alexandre Bourassa, Kevin J. Satzinger, Sabrina Hong, Catherine Erickson, Brian J. Lester, Kevin C. Miao, Alexander N. Korotkov, Julian Kelly, Zijun Chen, Paul V. Klimov

Measurement is an essential component of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate model-based readout optimization achieving low measurement errors while avoiding detrimental side-effects. For simultaneous and mid-circuit measurements across 17 qubits, we observe 1.5% error per qubit with a 500ns end-to-end duration and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions achieving a leakage rate limited by natural heating. This technique can scale to hundreds of qubits and be used to enhance the performance of error-correcting codes and near-term applications.

Design and characterization of a lumped element single-ended superconducting microwave parametric amplifier with on-chip flux bias line

Josh Mutus, Ted White, Evan Jeffrey, Daniel Sank, Rami Barends, Joerg Bochmann, Yu Chen, Zijun Chen, Ben Chiaro, Andrew Dunsworth, Julian Kelly, Anthony Megrant, Charles Neill, Peter O'Malley, Pedram Roushan, Amit Vainsencher, James Wenner, Irfan Siddiqi, Rajamani Vijayaraghavan, Andrew Cleland, John Martinis

We demonstrate a lumped-element Josephson parametric amplifier, using a single-ended design that includes an on-chip, high-bandwidth flux bias line. The amplifier can be pumped into its region of parametric gain through either the input port or through the flux bias line. Broadband amplification is achieved at a tunable frequency $ω/2 π$ between 5 to 7 GHz with quantum-limited noise performance, a gain-bandwidth product greater than 500 MHz, and an input saturation power in excess of -120 dBm. The bias line allows fast frequency tuning of the amplifier, with variations of hundreds of MHz over time scales shorter than 10 ns.

Resisting high-energy impact events through gap engineering in superconducting qubit arrays

Matt McEwen, Kevin C. Miao, Juan Atalaya, Alex Bilmes, Alex Crook, Jenna Bovaird, John Mark Kreikebaum, Nicholas Zobrist, Evan Jeffrey, Bicheng Ying, Andreas Bengtsson, Hung-Shen Chang, Andrew Dunsworth, Julian Kelly, Yaxing Zhang, Ebrahim Forati, Rajeev Acharya, Justin Iveland, Wayne Liu, Seon Kim, Brian Burkett, Anthony Megrant, Yu Chen, Charles Neill, Daniel Sank, Michel Devoret, Alex Opremcak

Quantum error correction (QEC) provides a practical path to fault-tolerant quantum computing through scaling to large qubit numbers, assuming that physical errors are sufficiently uncorrelated in time and space. In superconducting qubit arrays, high-energy impact events produce correlated errors, violating this key assumption. Following such an event, phonons with energy above the superconducting gap propagate throughout the device substrate, which in turn generate a temporary surge in quasiparticle (QP) density throughout the array. When these QPs tunnel across the qubits' Josephson junctions, they induce correlated errors. Engineering different superconducting gaps across the qubit's Josephson junctions provides a method to resist this form of QP tunneling. By fabricating all-aluminum transmon qubits with both strong and weak gap engineering on the same substrate, we observe starkly different responses during high-energy impact events. Strongly gap engineered qubits do not show any degradation in T1 during impact events, while weakly gap engineered qubits show events of correlated degradation in T1. We also show that strongly gap engineered qubits are robust to QP poisoning from increasing optical illumination intensity, whereas weakly gap engineered qubits display rapid degradation in coherence. Based on these results, gap engineering removes the threat of high-energy impacts to QEC in superconducting qubit arrays.

Noise-resilient Edge Modes on a Chain of Superconducting Qubits

Xiao Mi, Michael Sonner, Murphy Yuezhen Niu, Kenneth W. Lee, Brooks Foxen, Rajeev Acharya, Igor Aleiner, Trond I. Andersen, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Zijun Chen, Benjamin Chiaro, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Dripto M. Debroy, Sean Demura, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, Leslie Flores, Ebrahim Forati, Austin G. Fowler, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Matthew P. Harrigan, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, J. M. Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Joonho Lee, Lily Laws, Wayne Liu, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Matt McEwen, Bernardo Meurer Costa, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Alexis Morvan, Emily Mount, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Thomas E. O'Brien, Alex Opremcak, Andre Petukhov, Rebecca Potter, Chris Quintana, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Christopher Schuster, Michael J. Shearn, Vladimir Shvarts, Doug Strain, Yuan Su, Marco Szalay, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff-Heidweiller, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Hartmut Neven, Sergio Boixo, Anthony Megrant, Yu Chen, Julian Kelly, Vadim Smelyanskiy, Dmitry A. Abanin, Pedram Roushan

Computing prime factors with a Josephson phase qubit quantum processor

Erik Lucero, Rami Barends, Yu Chen, Julian Kelly, Matteo Mariantoni, Anthony Megrant, Peter O'Malley, Daniel Sank, Amit Vainsencher, James Wenner, Ted White, Yi Yin, Andrew N. Cleland, John M. Martinis

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5], however this has yet to be shown using solid state quantum bits (qubits). Two advantages of superconducting qubit architectures are the use of conventional microfabrication techniques, which allow straightforward scaling to large numbers of qubits, and a toolkit of circuit elements that can be used to engineer a variety of qubit types and interactions[6, 7]. Using a number of recent qubit control and hardware advances [7-13], here we demonstrate a nine-quantum-element solid-state QuP and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produces coherent interactions between five qubits and verify bi- and tripartite entanglement via quantum state tomography (QST) [8, 12, 14, 15]. In the final experiment, we run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. Improvements in the superconducting qubit coherence times and more complex circuits should provide the resources necessary to factor larger composite numbers and run more intricate quantum algorithms.

Measurement-induced entanglement and teleportation on a noisy quantum processor

Jesse C. Hoke, Matteo Ippoliti, Eliott Rosenberg, Dmitry Abanin, Rajeev Acharya, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Joseph C. Bardin, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Zijun Chen, Ben Chiaro, Desmond Chik, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Alejandro Grajales Dau, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Augustin Di Paolo, Ilya K. Drozdov, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Reza Fatemi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Raja Gosula, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Paula Heu, Markus R. Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Cody Jones, Pavol Juhas, Dvir Kafri, Kostyantyn Kechedzhi, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Lily Laws, Joonho Lee, Kenny W. Lee, Yuri D. Lensky, Brian J. Lester, Alexander T. Lill, Wayne Liu, Aditya Locharla, Orion Martin, Jarrod R. McClean, Matt McEwen, Kevin C. Miao, Amanda Mieszala, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Wojciech Mruczkiewicz, Matthew Neeley, Charles Neill, Ani Nersisyan, Michael Newman, Jiun H. Ng, Anthony Nguyen, Murray Nguyen, Murphy Yuezhen Niu, Tom E. O'Brien, Seun Omonije, Alex Opremcak, Andre Petukhov, Rebecca Potter, Leonid P. Pryadko, Chris Quintana, Charles Rocque, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vlad Shvarts, Jindra Skruzny, W. Clarke Smith, Rolando D. Somma, George Sterling, Douglas Strain, Marco Szalay, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Ted White, Bryan W. K. Woo, Cheng Xing, Z. Jamie. Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, Harmut Neven, Ryan Babbush, Dave Bacon, Sergio Boixo, Jeremy Hilton, Erik Lucero, Anthony Megrant, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Xiao Mi, Vedika Khemani, Pedram Roushan

Observation of Time-Crystalline Eigenstate Order on a Quantum Processor

Xiao Mi, Matteo Ippoliti, Chris Quintana, Ami Greene, Zijun Chen, Jonathan Gross, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Dripto Debroy, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Joonho Lee, Kenny Lee, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O\' Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Yuan Su, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Anthony Megrant, Julian Kelly, Yu Chen, S. L. Sondhi, Roderich Moessner, Kostyantyn Kechedzhi, Vedika Khemani, Pedram Roushan

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.