Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

Sergei V. Isakov, Matthew B. Hastings, Roger G. Melko

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.

Quantum annealing with more than one hundred qubits

Sergio Boixo, Troels F. Rønnow, Sergei V. Isakov, Zhihui Wang, David Wecker, Daniel A. Lidar, John M. Martinis, Matthias Troyer

Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with capabilities exceeding classical computers. A quantum annealer, in particular, solves hard optimisation problems by evolving a known initial configuration at non-zero temperature towards the ground state of a Hamiltonian encoding a given problem. Here, we present results from experiments on a 108 qubit D-Wave One device based on superconducting flux qubits. The strong correlations between the device and a simulated quantum annealer, in contrast with weak correlations between the device and classical annealing or classical spin dynamics, demonstrate that the device performs quantum annealing. We find additional evidence for quantum annealing in the form of small-gap avoided level crossings characterizing the hard problems. To assess the computational power of the device we compare it to optimised classical algorithms.

Quantum-Assisted Genetic Algorithm

James King, Masoud Mohseni, William Bernoudy, Alexandre Fréchette, Hossein Sadeghi, Sergei V. Isakov, Hartmut Neven, Mohammad H. Amin

Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers -- we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of non-local classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization.

Simulations of Quantum Circuits with Approximate Noise using qsim and Cirq

Sergei V. Isakov, Dvir Kafri, Orion Martin, Catherine Vollgraff Heidweiller, Wojciech Mruczkiewicz, Matthew P. Harrigan, Nicholas C. Rubin, Ross Thomson, Michael Broughton, Kevin Kissell, Evan Peters, Erik Gustafson, Andy C. Y. Li, Henry Lamm, Gabriel Perdue, Alan K. Ho, Doug Strain, Sergio Boixo

We introduce multinode quantum trajectory simulations with qsim, an open source high performance simulator of quantum circuits. qsim can be used as a backend of Cirq, a Python software library for writing quantum circuits. We present a novel delayed inner product algorithm for quantum trajectories which can result in an order of magnitude speedup for low noise simulation. We also provide tools to use this framework in Google Cloud Platform, with high performance virtual machines in a single mode or multinode setting. Multinode configurations are well suited to simulate noisy quantum circuits with quantum trajectories. Finally, we introduce an approximate noise model for Google's experimental quantum computing platform and compare the results of noisy simulations with experiments for several quantum algorithms on Google's Quantum Computing Service.

Classical antiferromagnet on a hyperkagome lattice

John M. Hopkinson, Sergei V. Isakov, Hae-Young Kee, Yong Baek Kim

Motivated by recent experiments on Na_4Ir_3O_8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This ``hyperkagome'' lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via ``order by disorder'', representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.

Fate of partial order on the trillium and distorted windmill lattices

Sergei V. Isakov, John M. Hopkinson, Hae-Young Kee

The classical Heisenberg model on the trillium and distorted windmill lattices exhibits a degenerate ground state within large-$N$ theory, where the degenerate wavevectors form a surface and line, in 3-dimensional space, respectively. We name such states partially ordered to represent the existence of long-range order along the direction normal to these degenerate manifolds. We investigate the effects of thermal fluctuations using Monte Carlo (MC) methods, and find a first order transition to a magnetically ordered state for both cases. We further show that the ordering on the distorted windmill lattice is due to order by disorder, while the ground state of the trillium lattice is unique. Despite these different routes to the realization of low temperature ordered phases, the static structure factors obtained by large-$N$ theory and MC simulations for each lattice show quantitative agreement in the cooperative paramagnetic regime at finite temperatures. This suggests that a remnant of the characteristic angle-dependent spin correlations of partial order remains above the transition temperatures for both lattices. The possible relevance of these results to $β$-Mn, CeIrSi, and MnSi is discussed.

What is the Computational Value of Finite Range Tunneling?

Vasil S. Denchev, Sergio Boixo, Sergei V. Isakov, Nan Ding, Ryan Babbush, Vadim Smelyanskiy, John Martinis, Hartmut Neven

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is $\sim 10^8$ times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to $\sim 10^8$ times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

Quantum order by disorder in a spin-one frustrated magnet on the kagome lattice

Sergei V. Isakov, Yong Baek Kim

We study the XXZ spin-one quantum magnet on the kagome lattice as an example where quantum fluctuations on highly degenerate classical ground states lead to various exotic quantum ground states. Previous studies have predicted several quantum phases, but different analytical approaches do not necessarily lead to the same physical picture. In this work, we use Quantum Monte Carlo computations to critically examine some of the predictions made in the string-net mean-field theory and the degenerate perturbation theory combined with duality analysis and effective field theory. It is found that the resulting phase diagram differs from some of the previous predictions. Further implications of our results to different analytical approaches are discussed.

Characterizing Quantum Supremacy in Near-Term Devices

Sergio Boixo, Sergei V. Isakov, Vadim N. Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J. Bremner, John M. Martinis, Hartmut Neven

A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits - the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.

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

Computational Role of Collective Tunneling in a Quantum Annealer

Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad Amin, Anatoly Smirnov, Masoud Mohseni, Hartmut Neven

Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We develop a theoretical model based on a NIBA Quantum Master Equation to describe the multiqubit dissipative tunneling effects under the complex noise characteristics of such quantum devices. We start by considering a computational primitive, an optimization problem consisting of just one global and one false minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the "critical" phase during the evolution where quantum tunneling "decides" the right path to solution. In a later stage dissipation facilitates the multiqubit tunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-Wave Two quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specifically, we provide an analysis of an optimization problem with sixteen qubits, demonstrating eight qubit tunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

Computational Role of Multiqubit Tunneling in a Quantum Annealer

Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad Amin, Anatoly Smirnov, Masoud Mohseni, Hartmut Neven

Quantum tunneling, a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself, has been hypothesized as an advantageous physical resource for optimization. Here we show that multiqubit tunneling plays a computational role in a currently available, albeit noisy, programmable quantum annealer. We develop a non-perturbative theory of open quantum dynamics under realistic noise characteristics predicting the rate of many-body dissipative quantum tunneling. We devise a computational primitive with 16 qubits where quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. Furthermore, we experimentally demonstrate that quantum tunneling can outperform thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. Our results indicate that many-body quantum phenomena could be used for finding better solutions to hard optimization problems.

Scaling analysis and instantons for thermally-assisted tunneling and Quantum Monte Carlo simulations

Zhang Jiang, Vadim N. Smelyanskiy, Sergei V. Isakov, Sergio Boixo, Guglielmo Mazzola, Matthias Troyer, Hartmut Neven

We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path integral Quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunnelling and QMC rates scale polynomially with the number of spins $N$ while a purely classical over-the-barrier activation rate scales exponentially with $N$.

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.

Quantum error correction below the surface code threshold

Rajeev Acharya, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, Craig Gidney, Dar Gilboa, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Alex Greene, Jonathan A. Gross, Steve Habegger, John Hall, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Francisco J. H. Heras, Stephen Heslin, Paula Heu, Oscar Higgott, Gordon Hill, Jeremy Hilton, George Holland, Sabrina Hong, Hsin-Yuan Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Stephen Jordan, Chaitali Joshi, Pavol Juhas, Dvir Kafri, Hui Kang, Amir H. Karamlou, Kostyantyn Kechedzhi, Julian Kelly, Trupti Khaire, Tanuj Khattar, Mostafa Khezri, Seon Kim, Paul V. Klimov, Andrey R. Klots, Bryce Kobrin, Pushmeet Kohli, Alexander N. Korotkov, Fedor Kostritsa, Robin Kothari, Borislav Kozlovskii, John Mark Kreikebaum, Vladislav D. Kurilovich, Nathan Lacroix, David Landhuis, Tiano Lange-Dei, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Loïck Le Guevel, Justin Ledford, Kenny Lee, Yuri D. Lensky, Shannon Leon, Brian J. Lester, Wing Yan Li, Yin Li, Alexander T. Lill, Wayne Liu, William P. Livingston, Aditya Locharla, Erik Lucero, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Fionn D. Malone, Ashley Maloney, Salvatore Mandrá, Leigh S. Martin, Steven Martin, Orion Martin, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Anthony Megrant, Xiao Mi, Kevin C. Miao, Amanda Mieszala, Reza Molavi, Sebastian Molina, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Hartmut Neven, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Thomas E. O'Brien, William D. Oliver, Alex Opremcak, Kristoffer Ottosson, Andre Petukhov, Alex Pizzuto, John Platt, Rebecca Potter, Orion Pritchard, Leonid P. Pryadko, Chris Quintana, Ganesh Ramachandran, Matthew J. Reagor, David M. Rhodes, Gabrielle Roberts, Eliott Rosenberg, Emma Rosenfeld, Pedram Roushan, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Andrew W. Senior, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Shraddha Singh, Volodymyr Sivak, Jindra Skruzny, Spencer Small, Vadim Smelyanskiy, W. Clarke Smith, Rolando D. Somma, Sofia Springer, George Sterling, Doug Strain, Jordan Suchard, Aaron Szasz, Alex Sztein, Douglas Thor, Alfredo Torres, M. Mert Torunbalci, Abeer Vaishnav, Justin Vargas, Sergey Vdovichev, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Steven Waltman, Shannon X. Wang, Brayden Ware, Kate Weber, Theodore White, Kristi Wong, Bryan W. K. Woo, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Noureldin Yosri, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist

Formation of robust bound states of interacting microwave photons

Alexis Morvan, Trond I. Andersen, Xiao Mi, Charles Neill, Andre Petukhov, Kostyantyn Kechedzhi, Dmitry Abanin, Rajeev Acharya, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, 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, 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, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Pavol Juhas, Dvir Kafri, Tanuj Khattar, Mostafa Khezri, Marika Kieferova, 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, Orion Martin, Jarrod R. McClean, Matt McEwen, Bernardo Meurer Costa, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Emily Mount, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Ani Nersisyan, Michael Newman, Anthony Nguyen, Murray Nguyen, Murphy Yuezhen Niu, Thomas E. O'Brien, Ricardo Olenewa, Alex Opremcak, Rebecca Potter, Chris Quintana, 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, W. Clarke Smith, George Sterling, Doug Strain, Yuan Su, Marco Szalay, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Theodore White, Cheng Xing, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Hartmut Neven, Sergio Boixo, Anthony Megrant, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Igor Aleiner, Lev B. Ioffe, Pedram Roushan

Fibonacci topological order from quantum nets

Paul Fendley, Sergei V. Isakov, Matthias Troyer

We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins around a face, around a vertex, and special "Jones-Wenzl" terms that serve to couple long loops together. We provide strong evidence for a gap by exact diagonalization, completing the list of ingredients necessary for topological order.

Néel to dimer transition in spin-S antiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

R. Ganesh, Sergei V. Isakov, Arun Paramekanti

We study the Néel to dimer transition driven by interlayer exchange coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear evidence that the transition is in the O(3) universality class for all S. Using bond operator mean field theory restricted to singlet and triplet states, we find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2, incorporating triplet-triplet interactions within a variational approach yields a critical interlayer coupling which agrees well with QMC. For higher spin, we argue that it is crucial to account for the high energy quintet modes, and show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S=1,3/2. We discuss the broad implications of our results for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).

Defining and detecting quantum speedup

Troels F. Rønnow, Zhihui Wang, Joshua Job, Sergio Boixo, Sergei V. Isakov, David Wecker, John M. Martinis, Daniel A. Lidar, Matthias Troyer

The development of small-scale digital and analog quantum devices raises the question of how to fairly assess and compare the computational power of classical and quantum devices, and of how to detect quantum speedup. Here we show how to define and measure quantum speedup in various scenarios, and how to avoid pitfalls that might mask or fake quantum speedup. We illustrate our discussion with data from a randomized benchmark test on a D-Wave Two device with up to 503 qubits. Comparing the performance of the device on random spin glass instances with limited precision to simulated classical and quantum annealers, we find no evidence of quantum speedup when the entire data set is considered, and obtain inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results for one particular benchmark do not rule out the possibility of speedup for other classes of problems and illustrate that quantum speedup is elusive and can depend on the question posed.