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Hartmut Neven

Hartmut Neven

Hartmut Neven is an Vice President of Engineering at Google. He is the founder and manager of the Quantum Artificial Intelligence lab. The objective of the lab is to fabricate quantum processors and develop novel quantum algorithms to dramatically accelerate computational tasks for machine intelligence. Previously, Hartmut was head of the Visual Search team. His team developed the visual search service which today is used by a large number of Google products including Image Search, Google Photos, YouTube, Street View and Google Goggles. His teams won a number of competitions designed to establish the best visual recognition software for faces (FERET 1996, FRVT 2002), objects (ImageNet 2014) and text (ICDAR 2013). Hartmut was also a co-founder of project Glass and led the team that built the first prototype. Prior to joining Google, Hartmut started two computer vision companies, the second one was acquired by Google in 2006. Hartmut obtained his Ph.D. in 1996 with a thesis on "Dynamics for vision-guided autonomous mobile robots". Then he became a research professor for computer science and theoretical neuroscience at the University of Southern California.
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    Preview abstract Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction [1, 2] 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%±0.016% compared to 3.028%±0.023%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10−6 logical error per round floor set by a single high-energy event (1.6 × 10−7 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, and illuminate the path to reaching the logical error rates required for computation. View details
    Purification-Based Quantum Error Mitigation of Pair-Correlated Electron Simulations
    Thomas E O'Brien
    Gian-Luca R. Anselmetti
    Fotios Gkritsis
    Vincent Elfving
    Stefano Polla
    William J. Huggins
    Oumarou Oumarou
    Kostyantyn Kechedzhi
    Dmitry Abanin
    Rajeev Acharya
    Igor Aleiner
    Richard Ross Allen
    Trond Ikdahl Andersen
    Kyle Anderson
    Markus Ansmann
    Frank Carlton Arute
    Kunal Arya
    Juan Atalaya
    Michael Blythe Broughton
    Bob Benjamin Buckley
    Alexandre Bourassa
    Leon Brill
    Tim Burger
    Nicholas Bushnell
    Jimmy Chen
    Yu Chen
    Benjamin Chiaro
    Desmond Chun Fung Chik
    Josh Godfrey Cogan
    Roberto Collins
    Paul Conner
    William Courtney
    Alex Crook
    Ben Curtin
    Ilya Drozdov
    Andrew Dunsworth
    Daniel Eppens
    Lara Faoro
    Edward Farhi
    Reza Fatemi
    Ebrahim Forati
    Brooks Riley Foxen
    William Giang
    Dar Gilboa
    Alejandro Grajales Dau
    Steve Habegger
    Michael C. Hamilton
    Sean Harrington
    Jeremy Patterson Hilton
    Trent Huang
    Ashley Anne Huff
    Sergei Isakov
    Justin Thomas Iveland
    Cody Jones
    Pavol Juhas
    Marika Kieferova
    Andrey Klots
    Alexander Korotkov
    Fedor Kostritsa
    John Mark Kreikebaum
    Dave Landhuis
    Pavel Laptev
    Kim Ming Lau
    Lily MeeKit Laws
    Joonho Lee
    Kenny Lee
    Alexander T. Lill
    Wayne Liu
    Orion Martin
    Trevor Johnathan Mccourt
    Anthony Megrant
    Xiao Mi
    Masoud Mohseni
    Shirin Montazeri
    Alexis Morvan
    Ramis Movassagh
    Wojtek Mruczkiewicz
    Charles Neill
    Ani Nersisyan
    Michael Newman
    Jiun How Ng
    Murray Nguyen
    Alex Opremcak
    Andre Gregory Petukhov
    Rebecca Potter
    Kannan Aryaperumal Sankaragomathi
    Christopher Schuster
    Mike Shearn
    Aaron Shorter
    Vladimir Shvarts
    Jindra Skruzny
    Vadim Smelyanskiy
    Clarke Smith
    Rolando Diego Somma
    Doug Strain
    Marco Szalay
    Alfredo Torres
    Guifre Vidal
    Jamie Yao
    Ping Yeh
    Juhwan Yoo
    Grayson Robert Young
    Yaxing Zhang
    Ningfeng Zhu
    Christian Gogolin
    Nature Physics (2023)
    Preview abstract An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations. View details
    Measurement-induced entanglement and teleportation on a noisy quantum processor
    Jesse Hoke
    Matteo Ippoliti
    Dmitry Abanin
    Rajeev Acharya
    Trond Andersen
    Markus Ansmann
    Frank Arute
    Kunal Arya
    Juan Atalaya
    Gina Bortoli
    Alexandre Bourassa
    Leon Brill
    Michael Broughton
    Bob Buckley
    Tim Burger
    Nicholas Bushnell
    Jimmy Chen
    Benjamin Chiaro
    Desmond Chik
    Josh Cogan
    Roberto Collins
    Paul Conner
    William Courtney
    Alex Crook
    Ben Curtin
    Alejo Grajales Dau
    Agustin Di Paolo
    ILYA Drozdov
    Andrew Dunsworth
    Daniel Eppens
    Edward Farhi
    Reza Fatemi
    Vinicius Ferreira
    Ebrahim Forati
    Brooks Foxen
    William Giang
    Dar Gilboa
    Raja Gosula
    Steve Habegger
    Michael Hamilton
    Monica Hansen
    Paula Heu
    Trent Huang
    Ashley Huff
    Bill Huggins
    Sergei Isakov
    Justin Iveland
    Cody Jones
    Pavol Juhas
    Kostyantyn Kechedzhi
    Marika Kieferova
    Alexei Kitaev
    Andrey Klots
    Alexander Korotkov
    Fedor Kostritsa
    John Mark Kreikebaum
    Dave Landhuis
    Pavel Laptev
    Kim Ming Lau
    Lily Laws
    Joonho Lee
    Kenny Lee
    Yuri Lensky
    Alexander Lill
    Wayne Liu
    Orion Martin
    Amanda Mieszala
    Shirin Montazeri
    Alexis Morvan
    Ramis Movassagh
    Wojtek Mruczkiewicz
    Charles Neill
    Ani Nersisyan
    Michael Newman
    JiunHow Ng
    Murray Ich Nguyen
    Tom O'Brien
    Seun Omonije
    Alex Opremcak
    Andre Petukhov
    Rebecca Potter
    Leonid Pryadko
    Charles Rocque
    Negar Saei
    Kannan Sankaragomathi
    Henry Schurkus
    Christopher Schuster
    Mike Shearn
    Aaron Shorter
    Noah Shutty
    Vladimir Shvarts
    Jindra Skruzny
    Clarke Smith
    Rolando Somma
    George Sterling
    Doug Strain
    Marco Szalay
    Alfredo Torres
    Guifre Vidal
    Cheng Xing
    Jamie Yao
    Ping Yeh
    Juhwan Yoo
    Grayson Young
    Yaxing Zhang
    Ningfeng Zhu
    Jeremy Hilton
    Anthony Megrant
    Yu Chen
    Vadim Smelyanskiy
    Xiao Mi
    Vedika Khemani
    Nature, vol. 622 (2023), 481–486
    Preview 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 the established paradigms for characterizing phases, either in or out of equilibrium. For present-day noisy intermediate-scale quantum (NISQ) processors, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study 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. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors. View details
    Quantum Simulation of Exact Electron Dynamics can be more Efficient than Classical Mean-Field Methods
    William J. Huggins
    Dominic W. Berry
    Shu Fay Ung
    Andrew Zhao
    David Reichman
    Andrew Baczewski
    Joonho Lee
    Nature Communications, vol. 14 (2023), pp. 4058
    Preview abstract Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage. View details
    Preview abstract Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it - one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoCo or P450. View details
    Noise-resilient Majorana Edge Modes on a Chain of Superconducting Qubits
    Alejandro Grajales Dau
    Alex Crook
    Alex Opremcak
    Alexa Rubinov
    Alexander Korotkov
    Alexandre Bourassa
    Alexei Kitaev
    Alexis Morvan
    Andre Gregory Petukhov
    Andrew Dunsworth
    Andrey Klots
    Anthony Megrant
    Ashley Anne Huff
    Benjamin Chiaro
    Bernardo Meurer Costa
    Bob Benjamin Buckley
    Brooks Foxen
    Charles Neill
    Christopher Schuster
    Cody Jones
    Daniel Eppens
    Dar Gilboa
    Dave Landhuis
    Dmitry Abanin
    Doug Strain
    Ebrahim Forati
    Edward Farhi
    Fedor Kostritsa
    Frank Carlton Arute
    Guifre Vidal
    Igor Aleiner
    Jamie Yao
    Jeremy Patterson Hilton
    Joao Basso
    John Mark Kreikebaum
    Joonho Lee
    Juan Atalaya
    Juhwan Yoo
    Justin Thomas Iveland
    Kannan Aryaperumal Sankaragomathi
    Kenny Lee
    Kim Ming Lau
    Kostyantyn Kechedzhi
    Kunal Arya
    Lara Faoro
    Leon Brill
    Marco Szalay
    Masoud Mohseni
    Michael Blythe Broughton
    Michael Newman
    Michel Henri Devoret
    Mike Shearn
    Nicholas Bushnell
    Orion Martin
    Paul Conner
    Pavel Laptev
    Ping Yeh
    Rajeev Acharya
    Rebecca Potter
    Reza Fatemi
    Roberto Collins
    Sergei Isakov
    Shirin Montazeri
    Steve Habegger
    Thomas E O'Brien
    Trent Huang
    Trond Ikdahl Andersen
    Vadim Smelyanskiy
    Vladimir Shvarts
    Wayne Liu
    William Courtney
    William Giang
    William J. Huggins
    Wojtek Mruczkiewicz
    Xiao Mi
    Yaxing Zhang
    Yu Chen
    Yuan Su
    Zijun Chen
    Science (2022) (to appear)
    Preview abstract Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the kicked Ising model which exhibits Majorana edge modes (MEMs) protected by a $\mathbb{Z}_2$-symmetry. Remarkably, we find that any multi-qubit Pauli operator overlapping with the MEMs exhibits a uniform decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This finding allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Spectroscopic measurements further indicate exponentially suppressed hybridization between the MEMs over larger system sizes, which manifests as a strong resilience against low-frequency noise. Our work elucidates the noise sensitivity of symmetry-protected edge modes in a solid-state environment. View details
    Direct Measurement of Nonlocal Interactions in the Many-Body Localized Phase
    Amit Vainsencher
    Andrew Dunsworth
    Anthony Megrant
    Ben Chiaro
    Brooks Foxen
    Charles Neill
    Dave Landhuis
    Fedor Kostritsa
    Frank Carlton Arute
    Jimmy Chen
    John Martinis
    Josh Mutus
    Kostyantyn Kechedzhi
    Kunal Arya
    Rami Barends
    Roberto Collins
    Trent Huang
    Vadim Smelyanskiy
    Yu Chen
    Physical Review Research, vol. 4 (2022), pp. 013148
    Preview abstract The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter. View details
    Preview abstract We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to nonergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure. View details
    Quantum advantage in learning from experiments
    Hsin-Yuan (Robert) Huang
    Michael Blythe Broughton
    Jordan Cotler
    Sitan Chen
    Jerry Li
    Masoud Mohseni
    Richard Kueng
    John Preskill
    Science, vol. 376 (2021), pp. 1182 - 1186
    Preview abstract Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature. View details
    Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits
    Lara Faoro
    Kunal Arya
    Andrew Dunsworth
    Trent Huang
    Frank Arute
    Bob B. Buckley
    Nicholas Bushnell
    Jimmy Chen
    Roberto Collins
    Alan R. Derk
    Sean Harrington
    Fedor Kostritsa
    Pavel Laptev
    Xiao Mi
    Shirin Montazeri
    Josh Mutus
    Charles Neill
    Alex Opremcak
    Nicholas Redd
    Vladimir Shvarts
    Jamie Yao
    Ping Yeh
    Juhwan Yoo
    Yu Chen
    Vadim Smelyanskiy
    John Martinis
    Anthony Megrant
    Rami Barends
    Nature Physics (2021)
    Preview abstract Scalable quantum computing can become a reality with error correction, provided that coherent qubits can be constructed in large arrays. The key premise is that physical errors can remain both small and sufficiently uncorrelated as devices scale, so that logical error rates can be exponentially suppressed. However, impacts from cosmic rays and latent radioactivity violate these assumptions. An impinging particle can ionize the substrate and induce a burst of quasiparticles that destroys qubit coherence throughout the device. High-energy radiation has been identified as a source of error in pilot superconducting quantum devices, but the effect on large-scale algorithms and error correction remains an open question. Elucidating the physics involved requires operating large numbers of qubits at the same rapid timescales necessary for error correction. Here, we use space- and time-resolved measurements of a large-scale quantum processor to identify bursts of quasiparticles produced by high-energy rays. We track the events from their initial localized impact as they spread, simultaneously and severely limiting the energy coherence of all qubits and causing chip-wide failure. Our results provide direct insights into the impact of these damaging error bursts and highlight the necessity of mitigation to enable quantum computing to scale. View details
    Preview abstract One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these algorithms based on connections to simple dynamics of quantum systems, quantum walks, and classical continuous relaxations. We focus on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement. This physical language, in combination with uniqueness results related to unitarity, allow us to identify some potential pitfalls from kinetic energy fundamentally opposing the goal of optimization. This is connected to effects from wavefunction confinement, phase randomization, and shadow defects lurking in the objective far away from the ideal solution. As an example, we explore the surprising deficiency of many quantum methods in solving uncoupled spin problems and how this is both predictive of performance on some more complex systems while immediately suggesting simple resolutions. Further examination of canonical problems like the Hamming ramp or bush of implications show that entanglement can be strictly detrimental to performance results from the underlying mechanism of solution in approaches like QAOA. Kinetic energy and graph Laplacian perspectives provide new insights to common initialization and optimal solutions in QAOA as well as new methods for more effective layerwise training. Connections to classical methods of continuous extensions, homotopy methods, and iterated rounding suggest new directions for research in quantum optimization. Throughout, we unveil many pitfalls and mechanisms in quantum optimization using a physical perspective, which aim to spur the development of novel quantum optimization algorithms and refinements. View details
    Preview abstract In this perspective we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best classical alternative. The challenge is that the computation must finish within a reasonable amount of time while being difficult enough that the small quantum scaling advantage would compensate for the large constant factor overheads associated with error correction. We compute several examples of such runtimes using state-of-the-art surface code constructions under a variety of assumptions. We conclude that quadratic speedups will not enable quantum advantage on early generations of such fault-tolerant devices unless there is a significant improvement in how we realize quantum error correction. While this conclusion persists even if we were to increase the rate of logical gates in the surface code by more than an order of magnitude, we also repeat this analysis for speedups by other polynomial degrees and find that quartic speedups look significantly more practical. View details
    Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
    Kevin Jeffery Sung
    Frank Carlton Arute
    Kunal Arya
    Juan Atalaya
    Rami Barends
    Michael Blythe Broughton
    Bob Benjamin Buckley
    Nicholas Bushnell
    Jimmy Chen
    Yu Chen
    Ben Chiaro
    Roberto Collins
    William Courtney
    Andrew Dunsworth
    Brooks Riley Foxen
    Rob Graff
    Steve Habegger
    Sergei Isakov
    Cody Jones
    Kostyantyn Kechedzhi
    Alexander Korotkov
    Fedor Kostritsa
    Dave Landhuis
    Pavel Laptev
    Martin Leib
    Mike Lindmark
    Orion Martin
    John Martinis
    Anthony Megrant
    Xiao Mi
    Masoud Mohseni
    Wojtek Mruczkiewicz
    Josh Mutus
    Charles Neill
    Florian Neukart
    Thomas E O'Brien
    Bryan O'Gorman
    A.G. Petukhov
    Harry Putterman
    Andrea Skolik
    Vadim Smelyanskiy
    Doug Strain
    Michael Streif
    Marco Szalay
    Amit Vainsencher
    Jamie Yao
    Leo Zhou
    Edward Farhi
    Nature Physics (2021)
    Preview abstract Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies. Here we demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the planar connectivity graph native to our hardware; however, we also apply the QAOA to the Sherrington–Kirkpatrick model and MaxCut, non-native problems that require extensive compilation to implement. For hardware-native problems, which are classically efficient to solve on average, we obtain an approximation ratio that is independent of problem size and observe that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size. Circuits involving several thousand gates still present an advantage over random guessing but not over some efficient classical algorithms. Our results suggest that it will be challenging to scale near-term implementations of the QAOA for problems on non-native graphs. As these graphs are closer to real-world instances, we suggest more emphasis should be placed on such problems when using the QAOA to benchmark quantum processors. View details
    Removing leakage-induced correlated errors in superconducting quantum error correction
    Jimmy Chen
    Juan Atalaya
    Frank Carlton Arute
    Kunal Arya
    Bob Benjamin Buckley
    Nicholas Bushnell
    Benjamin Chiaro
    Roberto Collins
    Andrew Dunsworth
    Brooks Riley Foxen
    Trent Huang
    Kostyantyn Kechedzhi
    Fedor Kostritsa
    Pavel Laptev
    Anthony Megrant
    Xiao Mi
    Josh Mutus
    Charles Neill
    Alexandru Paler
    Nick Redd
    Jamie Yao
    Ping Yeh
    Yu Chen
    Vadim Smelyanskiy
    John Martinis
    Alexander Korotkov
    Andre Gregory Petukhov
    Rami Barends
    Nature Communications, vol. 12 (2021), pp. 1761
    Preview abstract Quantum computing becomes scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, the unused high energy states of the qubits can become excited. In weakly nonlinear qubits, such as the superconducting transmon, these leakage states are long-lived and mobile, opening a path to errors that are correlated in space and time. The effects of leakage and its mitigation during quantum error correction remain an open question. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. It requires no additional hardware and combines speed, fidelity, and resilience to noise. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code scheme for quantum error correction. We investigate the accumulation and dynamics of leakage during the stabilizer codes. Using this protocol, we find lower rates of logical errors, and an improved scaling and stability of error suppression with qubits. This demonstration provides a key step on the path towards scalable quantum computing. View details
    Realizing topologically ordered states on a quantum processor
    Y.-J. Liu
    A. Smith
    C. Knapp
    M. Newman
    N. C. Jones
    Z. Chen
    X. Mi
    A. Dunsworth
    I. Aleiner
    F. Arute
    K. Arya
    J. Atalaya
    R. Barends
    J. Basso
    M. Broughton
    B. B. Buckley
    N. Bushnell
    B. Chiaro
    R. Collins
    W. Courtney
    A. R Derk
    D. Eppens
    L. Faoro
    E. Farhi
    B. Foxen
    A. Greene
    S. D. Harrington
    J. Hilton
    T. Huang
    W. J. Huggins
    S. V. Isakov
    K. Kechedzhi
    A. N. Korotkov
    F. Kostritsa
    D. Landhuis
    P. Laptev
    O. Martin
    M. Mohseni
    S. Montazeri
    W. Mruczkiewicz
    J. Mutus
    C. Neill
    T. E. O'Brien
    A. Opremcak
    B. Pato
    A. Petukhov
    V. Shvarts
    D. Strain
    M. Szalay
    Z. Yao
    P. Yeh
    J. Yoo
    A. Megrant
    Y. Chen
    V. Smelyanskiy
    A. Kitaev
    M. Knap
    F. Pollmann
    Science, vol. 374 (2021), pp. 1237-1241
    Preview abstract The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the emblematic toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy of Stopo ≈ −0.95 × ln 2 and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results illustrate the topological nature of these states and demonstrate their potential for implementing the surface code. View details
    Exponential suppression of bit or phase flip errors with repetitive quantum error correction
    Rami Barends
    Roberto Collins
    Sean Harrington
    Sergei Isakov
    Thomas E O'Brien
    Trent Huang
    Trevor Mccourt
    Vadim Smelyanskiy
    Vladimir Shvarts
    William Courtney
    Wojtek Mruczkiewicz
    Xiao Mi
    Yu Chen
    Alan Derk
    Alan Ho
    Alex Opremcak
    Alexander Korotkov
    Alexandre Bourassa
    Andre Gregory Petukhov
    Andrew Dunsworth
    Anthony Megrant
    Bálint Pató
    Benjamin Chiaro
    Brooks Riley Foxen
    Charles Neill
    Cody Jones
    Daniel Eppens
    Dave Landhuis
    Doug Strain
    Edward Farhi
    Eric Ostby
    Fedor Kostritsa
    Frank Carlton Arute
    Igor Aleiner
    Jamie Yao
    Jeremy Patterson Hilton
    Jimmy Chen
    Josh Mutus
    Juan Atalaya
    Kostyantyn Kechedzhi
    Kunal Arya
    Marco Szalay
    Masoud Mohseni
    Matt Trevithick
    Michael Broughton
    Michael Newman
    Nicholas Bushnell
    Nicholas Redd
    Orion Martin
    Pavel Laptev
    Ping Yeh
    Nature (2021)
    Preview abstract Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates below 10^-15, but state-of-the-art quantum platforms typically have physical error rates near 10^-3. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local, and that performance is maintained over many rounds of error correction, a major outstanding experimental challenge. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than 100x when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing. View details
    Tuning Quantum Information Scrambling on a 53-Qubit Processor
    Alan Derk
    Alan Ho
    Alex Opremcak
    Alexander Korotkov
    Alexandre Bourassa
    Andre Gregory Petukhov
    Andrew Dunsworth
    Anthony Megrant
    Bálint Pató
    Benjamin Chiaro
    Brooks Riley Foxen
    Charles Neill
    Cody Jones
    Daniel Eppens
    Dave Landhuis
    Doug Strain
    Edward Farhi
    Eric Ostby
    Fedor Kostritsa
    Frank Carlton Arute
    Igor Aleiner
    Jamie Yao
    Jeffrey Marshall
    Jeremy Patterson Hilton
    Jimmy Chen
    Josh Mutus
    Juan Atalaya
    Kostyantyn Kechedzhi
    Kunal Arya
    Marco Szalay
    Masoud Mohseni
    Matt Trevithick
    Michael Blythe Broughton
    Michael Newman
    Nicholas Bushnell
    Nicholas Redd
    Orion Martin
    Pavel Laptev
    Ping Yeh
    Rami Barends
    Roberto Collins
    Salvatore Mandra
    Sean Harrington
    Sergei Isakov
    Thomas E O'Brien
    Trent Huang
    Trevor Mccourt
    Vadim Smelyanskiy
    Vladimir Shvarts
    William Courtney
    Wojtek Mruczkiewicz
    Xiao Mi
    Yu Chen
    arXiv (2021)
    Preview abstract As entanglement in a quantum system grows, initially localized quantum information is spread into the exponentially many degrees of freedom of the entire system. This process, known as quantum scrambling, is computationally intensive to study classically and lies at the heart of several modern physics conundrums. Here, we characterize scrambling of different quantum circuits on a 53-qubit programmable quantum processor by measuring their out-of-time-order correlators (OTOCs). We observe that the spatiotemporal spread of OTOCs, as well as their circuit-to-circuit fluctuation, unravel in detail the time-scale and extent of quantum scrambling. Comparison with numerical results indicates a high OTOC measurement accuracy despite the large size of the quantum system. Our work establishes OTOC as an experimental tool to diagnose quantum scrambling at the threshold of being classically inaccessible. View details
    Power of data in quantum machine learning
    Hsin-Yuan (Robert) Huang
    Michael Blythe Broughton
    Masoud Mohseni
    Nature Communications, vol. 12 (2021), pp. 2631
    Preview abstract The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. View details
    Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
    Brooks Riley Foxen
    Charles Neill
    Andrew Dunsworth
    Ben Chiaro
    Anthony Megrant
    Jimmy Chen
    Rami Barends
    Frank Carlton Arute
    Kunal Arya
    Yu Chen
    Roberto Collins
    Edward Farhi
    Rob Graff
    Trent Huang
    Sergei Isakov
    Kostyantyn Kechedzhi
    Alexander Korotkov
    Fedor Kostritsa
    Dave Landhuis
    Xiao Mi
    Masoud Mohseni
    Josh Mutus
    Vadim Smelyanskiy
    Amit Vainsencher
    Jamie Yao
    John Martinis
    arXiv:2001.08343 (2020)
    Preview abstract Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite resources offered by existing noisy quantum hardware. Here, taking advantage of the strong adjustable coupling of gmon qubits, we demonstrate a continuous two qubit gate set that can provide a 5x reduction in circuit depth. We implement two gate families: an iSWAP-like gate to attain an arbitrary swap angle, $\theta$, and a CPHASE gate that generates an arbitrary conditional phase, $\phi$. Using one of each of these gates, we can perform an arbitrary two qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic Simulation, or fSim, gate set. We benchmark the fidelity of the iSWAP-like and CPHASE gate families as well as 525 other fSim gates spread evenly across the entire fSim($\theta$, $\phi$) parameter space achieving purity-limited average two qubit Pauli error of $3.8 \times 10^{-3}$ per fSim gate. View details
    Preview abstract Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through quantum sample learning: given samples from an n-qubit computation, can we learn the underlying quantum distribution using models with training parameters that scale polynomial in n under a fixed training time? We study four kinds of generative models: Deep Boltzmann machine (DBM), Generative Adversarial Networks (GANs), Long Short-Term Memory (LSTM) and Autoregressive GAN, on learning quantum data set generated by deep random circuits. We demonstrate the leading performance of LSTM in learning quantum samples, and thus the autoregressive structure present in the underlying quantum distribution from random quantum circuits. Both numerical experiments and a theoretical proof in the case of the DBM show exponentially growing complexity of learning-agent parameters required for achieving a fixed accuracy as n increases. Finally, we establish a connection between learnability and the complexity of generative models by benchmarking learnability against different sets of samples drawn from probability distributions of variable degrees of complexities in their quantum and classical representations. View details
    Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization
    Yuval Sanders
    Dominic W. Berry
    Pedro C. S. Costa
    Louis W. Tessler
    Nathan Wiebe
    PRX Quantum, vol. 1 (2020), pp. 020312
    Preview abstract Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum-accelerated simulated annealing including those using qubitization or Szegedy walks to quantize classical Markov chains and those simulating spectral-gap-amplified Hamiltonians encoding a Gibbs state. We also optimize fault-tolerant realizations of the adiabatic algorithm, quantum-enhanced population transfer, the quantum approximate optimization algorithm, and other approaches. Many of these methods are bottlenecked by calls to the same subroutines; thus, optimized circuits for those primitives should be of interest regardless of which heuristic is most effective in practice. We compile these bottlenecks for several families of optimization problems and report for how long and for what size systems one can perform these heuristics in the surface code given a range of resource budgets. Our results discourage the notion that any quantum optimization heuristic realizing only a quadratic speedup achieves an advantage over classical algorithms on modest superconducting qubit surface code processors without significant improvements in the implementation of the surface code. For instance, under quantum-favorable assumptions (e.g., that the quantum algorithm requires exactly quadratically fewer steps), our analysis suggests that quantum-accelerated simulated annealing requires roughly a day and a million physical qubits to optimize spin glasses that could be solved by classical simulated annealing in about 4 CPU-minutes. View details
    Preview abstract High performance quantum computing requires a calibration system that learns optimal control parameters much faster than system drift. In some cases, the learning procedure requires solving complex optimization problems that are non-convex, high-dimensional, highly constrained, and have astronomical search spaces. Such problems pose an obstacle for scalability since traditional global optimizers are often too inefficient and slow for even small-scale processors comprising tens of qubits. In this whitepaper, we introduce the Snake optimizer for efficiently and quickly solving such optimization problems by leveraging concepts in artificial intelligence, dynamic programming, and graph optimization. In practice, the Snake has been applied to optimize the frequencies at which quantum logic gates are implemented in frequency-tunable superconducting qubits. This application enabled state-of-the-art system performance on a 53 qubit quantum processor, serving as a key component of demonstrating quantum supremacy. Furthermore, since the Snake optimizer scales favorably with qubit number, is amenable to local re-optimization, and is parallelizable, it shows promise for optimizing much larger quantum processors. View details
    TensorFlow Quantum: A Software Framework for Quantum Machine Learning
    Michael Broughton
    Guillaume Verdon
    Trevor McCourt
    Antonio J. Martinez
    Jae Hyeon Yoo
    Sergei V. Isakov
    Philip Massey
    Ramin Halavati
    Alexander Zlokapa
    Evan Peters
    Owen Lockwood
    Andrea Skolik
    Sofiene Jerbi
    Vedran Djunko
    Martin Leib
    Michael Streif
    David Von Dollen
    Hongxiang Chen
    Chuxiang Cao
    Roeland Wiersema
    Hsin-Yuan Huang
    Alan K. Ho
    Masoud Mohseni
    (2020)
    Preview abstract We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage. View details
    Accurately computing electronic properties of materials using eigenenergies
    Alan Derk
    Alan Ho
    Alex Opremcak
    Alexander Korotkov
    Andre Gregory Petukhov
    Andrew Dunsworth
    Anthony Megrant
    Bálint Pató
    Benjamin Chiaro
    Bob Benjamin Buckley
    Brooks Riley Foxen
    Charles Neill
    Cody Jones
    Daniel Eppens
    Dave Landhuis
    Doug Strain
    Edward Farhi
    Eric Ostby
    Fedor Kostritsa
    Frank Carlton Arute
    Igor Aleiner
    Jamie Yao
    Jeremy Patterson Hilton
    Jimmy Chen
    Josh Mutus
    Juan Atalaya
    Juan Campero
    Kostyantyn Kechedzhi
    Kunal Arya
    Marco Szalay
    Masoud Mohseni
    Matt Jacob-Mitos
    Matt Trevithick
    Michael Blythe Broughton
    Michael Newman
    Nicholas Bushnell
    Nicholas Redd
    Orion Martin
    Pavel Laptev
    Ping Yeh
    Rami Barends
    Roberto Collins
    Sean Harrington
    Sergei Isakov
    Thomas E O'Brien
    Trent Huang
    Trevor Mccourt
    Vadim Smelyanskiy
    Vladimir Shvarts
    William Courtney
    William J. Huggins
    Wojtek Mruczkiewicz
    Xiao Mi
    Yu Chen
    arXiv preprint arXiv:2012.00921 (2020)
    Preview abstract A promising approach to study quantum materials is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using superconducting qubits, we provide an experimental blueprint for a programmable and accurate quantum matter simulator and demonstrate how to probe fundamental electronic properties. We illustrate the underlying method by reconstructing the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 radians, whereas typical energy scales are of order 1 radian. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 radians. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits. View details
    Preview abstract We introduce a fermion-to-qubit mapping using ternary trees. The mapping has a simple structure where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on log_3 (2n+1) qubits. We prove that the ternary-tree mapping is optimal in the sense that it is impossible to construct a Pauli operator in any fermion-to-qubit mapping which acts nontrivially on less than log_3 (2n+1) qubits. We apply this mapping to the problem of learning k-fermion reduced density matrix (RDM); a problem relevant in various quantum simulation applications. We show that using this mapping one can determine the elements of all k-fermion RDMs, to precision ε, by repeating a single quantum circuit for ~ (2n+1) k / ε^2 times. This result is based on a method we develop here that allows one to determine the elements of all k-qubit RDMs, to precision ε, by repeating a single quantum circuit for ~ 3k /ε^2 times, independent of the system size. This method improves over existing ones for determining qubit RDMs. View details
    Preview abstract Recent work has deployed linear combinations of unitaries techniques to significantly reduce the cost of performing fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve over those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energy per unit cell), as is often the goal for condensed-phase (e.g. solid-state) systems. In this context, simulations of the Hubbard model and plane wave electronic structure models with $N < 10^5$ fermionic modes can be performed with roughly O(1) and O(N^2) T complexities. We also perform numerics that reveal tradeoffs between the error of a Trotter step and Trotter step gate complexity across various implementations; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates using lattice surgery and assuming error rates of one part in a thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with only a few hundred thousand physical qubits. View details
    Preview abstract With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of error correction or mitigation that might enable practical applications before then. In this work, we consider the idea of post-processing error decoders using existing quantum codes, which are capable of mitigating errors on encoded logical qubits using classical post-processing with no complicated syndrome measurements or additional qubits beyond those used for the logical qubits. This greatly simplifies the experimental exploration of quantum codes on near-term devices, removing the need for locality of syndromes or fast feed-forward, allowing one to study performance aspects of codes on real devices. We provide a general construction equipped with a simple stochastic sampling scheme that does not depend explicitly on a number of terms that we extend to approximate projectors within a subspace. This theory then allows one to generalize to the correction of some logical errors in the code space, correction of some physical unencoded Hamiltonians without engineered symmetries, and corrections derived from approximate symmetries. In this work, we develop the theory of the method and demonstrate it on a simple example with the perfect [[5,1,3]] code, which exhibits a pseudo-threshold of p≈0.50 under a single qubit depolarizing channel applied to all qubits. We also provide a demonstration under the application of a logical operation and performance on an unencoded hydrogen molecule, which exhibits a significant improvement over the entire range of possible errors incurred under a depolarizing channel. View details
    Hartree-Fock on a Superconducting Qubit Quantum Computer
    Frank Carlton Arute
    Kunal Arya
    Rami Barends
    Michael Blythe Broughton
    Bob Benjamin Buckley
    Nicholas Bushnell
    Yu Chen
    Jimmy Chen
    Benjamin Chiaro
    Roberto Collins
    William Courtney
    Andrew Dunsworth
    Edward Farhi
    Brooks Riley Foxen
    Rob Graff
    Steve Habegger
    Alan Ho
    Trent Huang
    William J. Huggins
    Sergei Isakov
    Cody Jones
    Kostyantyn Kechedzhi
    Alexander Korotkov
    Fedor Kostritsa
    Dave Landhuis
    Pavel Laptev
    Mike Lindmark
    Orion Martin
    John Martinis
    Anthony Megrant
    Xiao Mi
    Masoud Mohseni
    Wojtek Mruczkiewicz
    Josh Mutus
    Charles Neill
    Thomas E O'Brien
    Eric Ostby
    Andre Gregory Petukhov
    Harry Putterman
    Vadim Smelyanskiy
    Doug Strain
    Kevin Jeffery Sung
    Marco Szalay
    Tyler Y. Takeshita
    Amit Vainsencher
    Nathan Wiebe
    Jamie Yao
    Ping Yeh
    Science, vol. 369 (2020), pp. 6507
    Preview abstract As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry which involve twice the number of qubits and more than ten times the number of gates as the largest prior experiments. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$, ${\rm H}_{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realize the Givens rotation approach to free fermion evolution, which we variationally optimize to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive corresponds to a rotation of the orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because free fermion evolutions are classically tractable to simulate, yet still generate highly entangled states over the computational basis, we use these experiments to benchmark the performance of our hardware while establishing a foundation for scaling up more complex correlated quantum simulations of chemistry. View details
    Preview abstract We present a quantum algorithm for simulating quantum chemistry with gate complexity Õ(η^{8/3}N^{1/3}),where η is the number of electrons and N is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity Õ(η^{2/3}N^{8/3}). We achieve our scaling in first quantization by performing simulation in the rotating frame of the kinetic operator using interaction picture techniques. Our algorithm is far more efficient than all prior approaches when N ≫ η, as is needed to suppress discretization error when representing molecules in the plane wave basis, or when simulating without the Born-Oppenheimer approximation. View details
    Diabatic gates for frequency-tunable superconducting qubits
    Rami Barends
    A.G. Petukhov
    Yu Chen
    Kostyantyn Kechedzhi
    Roberto Collins
    Frank Carlton Arute
    Kunal Arya
    Jimmy Chen
    Ben Chiaro
    Andrew Dunsworth
    Brooks Foxen
    Rob Graff
    Trent Huang
    Fedor Kostritsa
    Dave Landhuis
    Anthony Megrant
    Xiao Mi
    Josh Mutus
    Charles Neill
    Eric Ostby
    Amit Vainsencher
    Jamie Yao
    Ping Yeh
    Vadim Smelyanskiy
    John Martinis
    Physical Review Letters, vol. 123 (2019), pp. 210501
    Preview abstract We demonstrate diabatic two-qubit gates with Pauli error rates down to 4.3(2)*10^{-3} in as fast as 18 ns using frequency-tunable superconducting qubits. This is achieved by synchronizing the entangling parameters with minima in the leakage channel. The synchronization shows a landscape in gate parameter space that agrees with model predictions and facilitates robust tune-up. We test both iSWAP-like and CPHASE gates with cross-entropy benchmarking. The presented approach can be extended to multibody operations as well. View details
    Quantum Simulation of the Sachdev-Ye-Kitaev Model by Asymmetric Qubitization
    Dominic W. Berry
    Physical Review A Rapid Communication, vol. 99 (2019), 040301(R)
    Preview abstract We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with $N$ Majorana modes for time $t$ to precision $\epsilon$ with gate complexity ${\cal O}(N^{7/2} t + N^{5/2} \log(1 / \epsilon) / \log\log(1/\epsilon))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\epsilon$ and large polynomial improvement in $N$ and $t$ over prior state-of-the-art algorithms which scale as ${\cal O}(N^{10} t^2 / \epsilon)$. Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian $H$ as an asymmetric projection of a signal oracle $U$ onto two different signal states prepared by distinct state oracles, $A\ket{0} \mapsto \ket{A}$ and $B\ket{0} \mapsto \ket{B}$, such that $H = \bra{B} U \ket{A}$. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing $B$ using only Hadamard gates and realizing $A$ as a random quantum circuit. View details
    Preview abstract Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization heuristics that ensure rapid and consistent convergence to local minima of the parameterized quantum circuit landscape. In this work, we train classical neural networks to assist in the quantum learning process, also know as meta-learning, to rapidly find approximate optima in the parameter landscape for several classes of quantum variational algorithms. Specifically, we train classical recurrent neural networks to find approximately optimal parameters within a small number of queries of the cost function for the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut, QAOA for Sherrington-Kirkpatrick Ising model, and for a Variational Quantum Eigensolver for the Hubbard model. By initializing other optimizers at parameter values suggested by the classical neural network, we demonstrate a significant improvement in the total number of optimization iterations required to reach a given accuracy. We further demonstrate that the optimization strategies learned by the neural network generalize well across a range of problem instance sizes. This opens up the possibility of training on small, classically simulatable problem instances, in order to initialize larger, classically intractably simulatable problem instances on quantum devices, thereby significantly reducing the number of required quantum-classical optimization iterations. View details
    Preview abstract Implementation of an error corrected quantum computer is believed to require a quantum processor with on the order of a million or more physical qubits and, in order to run such a processor, a quantum control system of similar scale will be required. Such a controller will need to be integrated within the cryogenic system and in close proximity with the quantum processor in order to make such a system practical. Here, we present a prototype cryogenic CMOS quantum controller designed in a 28-nm bulk CMOS process and optimized to implement a 4-bit XY gate instruction set for transmon qubits. After introducing the transmon qubit, including a discussion of how it is controlled, design considerations are discussed, with an emphasis on error rates and scalability. The circuit design is then discussed. Cryogenic performance of the underlying technology is presented and the results of several quantum control experiments carried out using the integrated controller are described. The paper ends with a comparison to the state of the art. It has been shown that the quantum control IC achieves comparable performance with a conventional rack mount control system while dissipating less than 2mW of total AC and DC power and requiring a digital data stream of less than 500 Mb/s. View details
    A 28nm Bulk-CMOS 4-to-8GHz <2mW Cryogenic Pulse Modulator for Scalable Quantum Computing
    Trent Huang
    Rami Barends
    Kunal Arya
    Ben Chiaro
    Jimmy Chen
    Yu Chen
    Andrew Dunsworth
    Brooks Foxen
    Rob Graff
    Josh Mutus
    Anthony Megrant
    Charles Neill
    Amit Vainsencher
    John Martinis
    Proceedings of the 2019 International Solid State Circuits Conference, IEEE, pp. 456-458
    Preview abstract Future quantum computing systems will require cryogenic integrated circuits to control and measure millions of qubits. In this paper, we report design and measurement of a prototype cryogenic CMOS integrated circuit that has been optimized for the control of transmon qubits. The circuit has been integrated into a quantum measurement setup and its performance has been validated through multiple quantum control experiments. View details
    Quantum Supremacy using a Programmable Superconducting Processor
    Frank Arute
    Kunal Arya
    Rami Barends
    Rupak Biswas
    Fernando Brandao
    David Buell
    Yu Chen
    Jimmy Chen
    Ben Chiaro
    Roberto Collins
    William Courtney
    Andrew Dunsworth
    Edward Farhi
    Brooks Foxen
    Austin Fowler
    Rob Graff
    Keith Guerin
    Steve Habegger
    Michael Hartmann
    Alan Ho
    Trent Huang
    Travis Humble
    Sergei Isakov
    Kostyantyn Kechedzhi
    Sergey Knysh
    Alexander Korotkov
    Fedor Kostritsa
    Dave Landhuis
    Mike Lindmark
    Dmitry Lyakh
    Salvatore Mandrà
    Anthony Megrant
    Xiao Mi
    Kristel Michielsen
    Masoud Mohseni
    Josh Mutus
    Charles Neill
    Eric Ostby
    Andre Petukhov
    Eleanor G. Rieffel
    Vadim Smelyanskiy
    Kevin Jeffery Sung
    Matt Trevithick
    Amit Vainsencher
    Benjamin Villalonga
    Z. Jamie Yao
    Ping Yeh
    John Martinis
    Nature, vol. 574 (2019), 505–510
    Preview abstract The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. View details
    Preview abstract Fermion-to-qubit mappings that preserve geometric locality are especially useful for simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. They avoid the overhead associated with geometric nonlocal parity terms in mappings such as the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. As a result, they often provide quantum circuits with lower depth and gate complexity. In such encodings, fermionic states are encoded in the common +1 eigenspace of a set of stabilizers, akin to stabilizer quantum error-correcting codes. Here, we discuss several known geometric locality-preserving mappings and their abilities to correct and detect single-qubit errors. We introduce a geometric locality-preserving map, whose stabilizers correspond to products of Majorana operators on closed paths of the fermionic hopping graph. We show that our code, which we refer to as the Majorana loop stabilizer code (MLSC) can correct all single-qubit errors on a two-dimensional square lattice, while previous geometric locality-preserving codes can only detect single-qubit errors on the same lattice. Compared to existing codes, the MLSC maps the relevant fermionic operators to lower-weight qubit operators despite having higher code distance. Going beyond lattice models, we demonstrate that the MLSC is compatible with state-of-the-art algorithms for simulating quantum chemistry, and can offer those simulations the same error-correction properties without additional asymptotic overhead. These properties make the MLSC a promising candidate for error-mitigated quantum simulations of fermions on near-term devices View details
    Characterizing Quantum Supremacy in Near-Term Devices
    Sergei Isakov
    Vadim Smelyanskiy
    Michael J. Bremner
    John Martinis
    Nature Physics, vol. 14 (2018), 595–600
    Preview abstract A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy. We extend previous results in computational complexity to argue that this sampling task must take exponential time in a classical computer. We introduce cross-entropy benchmarking to obtain the experimental fidelity of complex multiqubit dynamics. This can be estimated and extrapolated to give a success metric for a quantum supremacy demonstration. We study the computational cost of relevant classical algorithms and conclude that quantum supremacy can be achieved with circuits in a two-dimensional lattice of 7 × 7 qubits and around 40 clock cycles. This requires an error rate of around 0.5% for two-qubit gates (0.05% for one-qubit gates), and it would demonstrate the basic building blocks for a fault-tolerant quantum computer View details
    Preview abstract Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied. View details
    Low-Depth Quantum Simulation of Materials
    Nathan Wiebe
    James McClain
    Garnet Chan
    Physical Review X, vol. 8 (2018), pp. 011044
    Preview abstract Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ molecular orbitals, leading to Hamiltonians with ${\cal O}(N^4)$ second-quantized terms. To avoid this overhead, we introduce basis functions which diagonalize the periodized Coulomb operator, providing Hamiltonians for condensed phase systems with $N^2$ second-quantized terms. Using this representation we can implement single Trotter steps of the Hamiltonians with gate depth of ${\cal O}(N)$ on a planar lattice of qubits -- a quartic improvement over prior methods. Special properties of our basis allow us to apply Trotter based simulations with planar circuit depth in $\widetilde{\cal O}(N^{7/2} / \epsilon^{1/2})$ and Taylor series methods with circuit size $\widetilde{\cal O}(N^{11/3})$, where $\epsilon$ is target precision. Variational algorithms also require significantly fewer measurements to find the mean energy using our representation, ameliorating a primary challenge of that approach. We conclude with a proposal to simulate the uniform electron gas (jellium) using a linear depth variational ansatz realizable on near-term quantum devices with planar connectivity. From these results we identify simulation of low-density jellium as an ideal first target for demonstrating quantum supremacy in electronic structure. View details
    Preview abstract High-fidelity control of qubits requires precisely tuned control parameters. Typically, these param- eters are found through a series of bootstrapped calibration experiments which successively acquire more accurate information about a physical qubit. However, optimal parameters are typically dif- ferent between devices and can also drift in time, which begets the need for an efficient calibration strategy. Here, we introduce a framework to understand the relationship between calibrations as a directed graph. With this approach, calibration is reduced to a graph traversal problem that is automatable and extensible. View details
    Fluctuations of Energy-Relaxation Times in Superconducting Qubits
    Jimmy Chen
    Anthony Megrant
    Rami Barends
    Kunal Arya
    Ben Chiaro
    Yu Chen
    Andrew Dunsworth
    Brooks Foxen
    Rob Graff
    Trent Huang
    Josh Mutus
    Charles Neill
    Amit Vainsencher
    Jim Wenner
    Vadim Smelyanskiy
    John Martinis
    Physical Review Letters, vol. 121 (2018), pp. 090502
    Preview abstract Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design and fabrication. View details
    Preview abstract We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use quantum phase estimation to sample states in the Hamiltonian eigenbasis with optimal query complexity O(lambda / epsilon) where lambda is an absolute sum of Hamiltonian coefficients and epsilon is target precision. For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T gate complexity O(N + \log (1/epsilon)) where N is number of orbitals in the basis. Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the classically intractable regime. Compiling to surface code fault-tolerant gates and assuming per gate error rates of one part in a thousand reveals that one can error-correct phase estimation on interesting instances of these problems beyond the current capabilities of classical methods using only a few times more qubits than would be required for magic state distillation. View details
    Preview abstract For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper, we derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is nonperturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the interqubit coupling, including nonstoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer approximation. View details
    Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
    Yu Chen
    Andre Petukhov
    Ben Chiaro
    Anthony Megrant
    Rami Barends
    Brooks Campbell
    Zijun Chen
    Andrew Dunsworth
    Rob Graff
    Josh Mutus
    Charles Neill
    Alireza Shabani
    Vadim Smelyanskiy
    Amit Vainsencher
    Jim Wenner
    John Martinis
    Phys. Rev. Lett., vol. 118 (2017), pp. 057702
    Preview abstract By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around 2kT/h ≈ 1GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component displays a 1/T dependence below 100 mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells. View details
    Commercialize Quantum Technologies in Five Years
    Masoud Mohseni
    Peter Read
    Vadim Smelyanskiy
    John Martinis
    Nature, vol. 543 (2017), 171–174
    Preview abstract Masoud Mohseni, Peter Read, Hartmut Neven and colleagues at Google's Quantum AI Laboratory set out investment opportunities on the road to the ultimate quantum machines. View details
    Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
    Yu Chen
    Andre Petukhov
    Ben Chiaro
    Anthony Megrant
    Rami Barends
    Brooks Campbell
    Zijun Chen
    Andrew Dunsworth
    Rob Graff
    Josh Mutus
    Charles Neill
    Alireza Shabani
    Vadim Smelyanskiy
    Amit Vainsencher
    Jim Wenner
    John Martinis
    Physical Review Letter, vol. 118 (2017), pp. 057702
    Preview abstract By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around 2kBT /h ≈ 1 GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component displays a 1/T dependence below 100 mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells. View details
    Chiral Ground-State Currents of Interacting Photons in a Synthetic Magnetic Field
    Charles Neill
    Anthony Megrant
    Yu Chen
    Rami Barends
    Brooks Campbell
    Zijun Chen
    Ben Chiaro
    Andrew Dunsworth
    Josh Mutus
    Amit Vainsencher
    Jim Wenner
    Eliot Kapit
    John Martinis
    Nature Physics, vol. 13 (2017), pp. 146-151
    Preview abstract The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields. Generating these phases in an engineered system could provide deeper insight into their nature. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall phenomena. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions through the creation of photon vacancies, or "holes", which circulate in the opposite direction. The combination of these key elements results in chiral ground-state currents. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons. View details
    Digitized Adiabatic Quantum Computing with a Superconducting Circuit
    Rami Barends
    Alireza Shabani
    Lucas Lamata
    Antonio Mezzacapo
    Urtzi Las Heras
    Brooks Campbell
    Yu Chen
    Zijun Chen
    Ben Chiaro
    Andrew Dunsworth
    Anthony Megrant
    Josh Mutus
    Charles Neill
    Enrique Solano
    Jim Wenner
    Amit Vainsencher
    John Martinis
    Nature, vol. 534 (2016), pp. 222-226
    Preview abstract A major challenge in quantum computing is to solve general problems with limited physical hardware. Here, we implement digitized adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital approach, using a superconducting circuit with nine qubits. We probe the adiabatic evolutions, and quantify the success of the algorithm for random spin problems. We find that the system can approximate the solutions to both frustrated Ising problems and problems with more complex interactions, with a performance that is comparable. The presented approach is compatible with small-scale systems as well as future error-corrected quantum computers. View details
    Preview abstract The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is O(Δ2), where Δ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture. View details
    What is the Computational Value of Finite Range Tunneling?
    Sergei Isakov
    Vadim Smelyanskiy
    John Martinis
    Physical Review X, vol. 6 (2016), pp. 031015
    Preview abstract 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 ~1e8 times faster than SA running on a single processor core. We also compare physical QA with the quantum Monte Carlo algorithm, 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 ~ 1e8 times faster than an optimized implementation of the quantum Monte Carlo algorithm on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a time scale comparable to the D-Wave 2X. However, it is well known that such solvers will become ineffective for sufficiently dense connectivity graphs. 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 algorithms designed to simulate QA scale better than SA. We discuss the implications of these findings for the design of next-generation quantum annealers. View details
    Computational multiqubit tunnelling in programmable quantum annealers
    Mohammad H Amin
    Anatoly Yu Smirnov
    Masoud Mohseni
    Vadim N Smelyanskiy
    Alireza Shabani
    Sergei V Isakov
    Mark Dykman
    Nature Communications, vol. 7 (2016)
    Preview abstract Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. View details
    Scalable Quantum Simulation of Molecular Energies
    Ian Kivlichan
    Jonathan Romero
    Rami Barends
    Andrew Tranter
    Brooks Campbell
    Yu Chen
    Zijun Chen
    Ben Chiaro
    Andrew Dunsworth
    Anthony Megrant
    Josh Mutus
    Charles Neil
    Jim Wenner
    Amit Vainsencher
    Peter Coveney
    Peter Love
    Alán Aspuru-Guzik
    John Martinis
    Physical Review X, vol. 6 (2016), pp. 031007
    Preview abstract We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms. First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver. Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result. Second, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation. We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors. This error tolerance inspires hope that variational quantum simulations of classically intractable molecules may be viable in the near future. View details
    Bayesian Sampling using Stochastic Gradient Thermostats
    Youhan Fang
    Changyou Chen
    Robert Skeel
    Advances in Neural Information Processing Systems (2014), pp. 3203-3211
    Preview abstract Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory. View details
    Large-Scale Object Classification Using Label Relation Graphs
    Jia Deng
    Yangqing Jia
    Andrea Frome
    Samy Bengio
    Yuan Li
    European Conference on Computer Vision (2014)
    Preview abstract . In this paper we study how to perform object classification in a principled way that exploits the rich structure of real world labels. We develop a new model that allows encoding of flexible relations between labels. We introduce Hierarchy and Exclusion (HEX) graphs, a new formalism that captures semantic relations between any two labels applied to the same object: mutual exclusion, overlap and subsumption. We then provide rigorous theoretical analysis that illustrates properties of HEX graphs such as consistency, equivalence, and computational implications of the graph structure. Next, we propose a probabilistic classification model based on HEX graphs and show that it enjoys a number of desirable properties. Finally, we evaluate our method using a large-scale benchmark. Empirical results demonstrate that our model can signifi- cantly improve object classification by exploiting the label relations. View details
    Preview abstract Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples. View details
    Large-scale Privacy Protection in Google Street View
    Andrea Frome
    German Cheung
    Ahmad Abdulkader
    Marco Zennaro
    Bo Wu
    Luc Vincent
    IEEE International Conference on Computer Vision (2009)
    Preview abstract The last two years have witnessed the introduction and rapid expansion of products based upon large, systematically-gathered, street-level image collections, such as Google Street View, EveryScape, and Mapjack. In the process of gathering images of public spaces, these projects also capture license plates, faces, and other information considered sensitive from a privacy standpoint. In this work, we present a system that addresses the challenge of automatically detecting and blurring faces and license plates for the purpose of privacy protection in Google Street View. Though some in the field would claim face detection is "solved", we show that state-of-the-art face detectors alone are not sufficient to achieve the recall desired for large-scale privacy protection. In this paper we present a system that combines a standard sliding-window detector tuned for a high recall, low-precision operating point with a fast post-processing stage that is able to remove additional false positives by incorporating domain-specific information not available to the sliding-window detector. Using a completely automatic system, we are able to sufficiently blur more than 89% of faces and 94-96% of license plates in evaluation sets sampled from Google Street View imagery. The full paper will appear from IEEE. View details
    Tour the world: a technical demonstration of a web-scale landmark recognition engine
    Yan-Tao Zheng
    Ulrich Buddemeier
    Fernando Brucher
    Tat-Seng Chua
    MM '09: Proceedings of the seventeen ACM international conference on Multimedia, ACM, New York, NY, USA (2009), pp. 961-962
    Preview
    Tour the World: building a web-scale landmark recognition engine
    Yantao Zheng
    Ulrich Buddemeier
    Fernando Brucher
    Tat-Seng Chua
    International Conference on Computer Vision and Pattern Recognition (CVPR) (2009)
    Preview
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