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Quantum supremacy using a programmable superconducting processor

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Frank Arute
Frank Arute
Frank Arute
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Kunal Arya
Kunal Arya
Kunal Arya
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Ryan Babbush at Harvard University
Ryan Babbush
Dave Bacon
Dave Bacon
Dave Bacon
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Abstract and Figures

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor¹. 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 qubits2–7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2⁵³ (about 10¹⁶). 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 supremacy8–14 for this specific computational task, heralding a much-anticipated computing paradigm.
The Sycamore processor a, Layout of processor, showing a rectangular array of 54 qubits (grey), each connected to its four nearest neighbours with couplers (blue). The inoperable qubit is outlined. b, Photograph of the Sycamore chip.
The Sycamore processor a, Layout of processor, showing a rectangular array of 54 qubits (grey), each connected to its four nearest neighbours with couplers (blue). The inoperable qubit is outlined. b, Photograph of the Sycamore chip.
… 
System-wide Pauli and measurement errors a, Integrated histogram (empirical cumulative distribution function, ECDF) of Pauli errors (black, green, blue) and readout errors (orange), measured on qubits in isolation (dotted lines) and when operating all qubits simultaneously (solid). The median of each distribution occurs at 0.50 on the vertical axis. Average (mean) values are shown below. b, Heat map showing single- and two-qubit Pauli errors e1 (crosses) and e2 (bars) positioned in the layout of the processor. Values are shown for all qubits operating simultaneously.
System-wide Pauli and measurement errors a, Integrated histogram (empirical cumulative distribution function, ECDF) of Pauli errors (black, green, blue) and readout errors (orange), measured on qubits in isolation (dotted lines) and when operating all qubits simultaneously (solid). The median of each distribution occurs at 0.50 on the vertical axis. Average (mean) values are shown below. b, Heat map showing single- and two-qubit Pauli errors e1 (crosses) and e2 (bars) positioned in the layout of the processor. Values are shown for all qubits operating simultaneously.
… 
Control operations for the quantum supremacy circuits a, Example quantum circuit instance used in our experiment. Every cycle includes a layer each of single- and two-qubit gates. The single-qubit gates are chosen randomly from {X,Y,W}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\sqrt{X},\sqrt{Y},\sqrt{W}\}$$\end{document}, where W=(X+Y)/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W=(X+Y)/\sqrt{2}$$\end{document} and gates do not repeat sequentially. The sequence of two-qubit gates is chosen according to a tiling pattern, coupling each qubit sequentially to its four nearest-neighbour qubits. The couplers are divided into four subsets (ABCD), each of which is executed simultaneously across the entire array corresponding to shaded colours. Here we show an intractable sequence (repeat ABCDCDAB); we also use different coupler subsets along with a simplifiable sequence (repeat EFGHEFGH, not shown) that can be simulated on a classical computer. b, Waveform of control signals for single- and two-qubit gates.
Control operations for the quantum supremacy circuits a, Example quantum circuit instance used in our experiment. Every cycle includes a layer each of single- and two-qubit gates. The single-qubit gates are chosen randomly from {X,Y,W}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\sqrt{X},\sqrt{Y},\sqrt{W}\}$$\end{document}, where W=(X+Y)/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W=(X+Y)/\sqrt{2}$$\end{document} and gates do not repeat sequentially. The sequence of two-qubit gates is chosen according to a tiling pattern, coupling each qubit sequentially to its four nearest-neighbour qubits. The couplers are divided into four subsets (ABCD), each of which is executed simultaneously across the entire array corresponding to shaded colours. Here we show an intractable sequence (repeat ABCDCDAB); we also use different coupler subsets along with a simplifiable sequence (repeat EFGHEFGH, not shown) that can be simulated on a classical computer. b, Waveform of control signals for single- and two-qubit gates.
… 
Demonstrating quantum supremacy a, Verification of benchmarking methods. ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} values for patch, elided and full verification circuits are calculated from measured bitstrings and the corresponding probabilities predicted by classical simulation. Here, the two-qubit gates are applied in a simplifiable tiling and sequence such that the full circuits can be simulated out to n = 53, m = 14 in a reasonable amount of time. Each data point is an average over ten distinct quantum circuit instances that differ in their single-qubit gates (for n = 39, 42 and 43 only two instances were simulated). For each n, each instance is sampled with Ns of 0.5–2.5 million. The black line shows the predicted ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} based on single- and two-qubit gate and measurement errors. The close correspondence between all four curves, despite their vast differences in complexity, justifies the use of elided circuits to estimate fidelity in the supremacy regime. b, Estimating ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} in the quantum supremacy regime. Here, the two-qubit gates are applied in a non-simplifiable tiling and sequence for which it is much harder to simulate. For the largest elided data (n = 53, m = 20, total Ns = 30 million), we find an average ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} > 0.1% with 5σ confidence, where σ includes both systematic and statistical uncertainties. The corresponding full circuit data, not simulated but archived, is expected to show similarly statistically significant fidelity. For m = 20, obtaining a million samples on the quantum processor takes 200 seconds, whereas an equal-fidelity classical sampling would take 10,000 years on a million cores, and verifying the fidelity would take millions of years.
Demonstrating quantum supremacy a, Verification of benchmarking methods. ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} values for patch, elided and full verification circuits are calculated from measured bitstrings and the corresponding probabilities predicted by classical simulation. Here, the two-qubit gates are applied in a simplifiable tiling and sequence such that the full circuits can be simulated out to n = 53, m = 14 in a reasonable amount of time. Each data point is an average over ten distinct quantum circuit instances that differ in their single-qubit gates (for n = 39, 42 and 43 only two instances were simulated). For each n, each instance is sampled with Ns of 0.5–2.5 million. The black line shows the predicted ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} based on single- and two-qubit gate and measurement errors. The close correspondence between all four curves, despite their vast differences in complexity, justifies the use of elided circuits to estimate fidelity in the supremacy regime. b, Estimating ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} in the quantum supremacy regime. Here, the two-qubit gates are applied in a non-simplifiable tiling and sequence for which it is much harder to simulate. For the largest elided data (n = 53, m = 20, total Ns = 30 million), we find an average ℱXEB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal F} }_{{\rm{XEB}}}$$\end{document} > 0.1% with 5σ confidence, where σ includes both systematic and statistical uncertainties. The corresponding full circuit data, not simulated but archived, is expected to show similarly statistically significant fidelity. For m = 20, obtaining a million samples on the quantum processor takes 200 seconds, whereas an equal-fidelity classical sampling would take 10,000 years on a million cores, and verifying the fidelity would take millions of years.
… 
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Nature | Vol 574 | 24 OCTOBER 2019 | 505
Article
Quantum supremacy using a programmable
superconducting processor
Frank Arute1, Kunal Arya1, Ryan Babbush1, Dave Bacon1, Joseph C. Bardin1,2, Rami Barends1,
Rupak Biswas3, Sergio Boixo1, Fernando G. S. L. Brandao1,4, David A. Buell1, Brian Burkett1,
Yu Chen1, Zijun Chen1, Ben Chiaro5, Roberto Collins1, William Courtney1, Andrew Dunsworth1,
Edward Farhi1, Brooks Foxen1,5, Austin Fowler1, Craig Gidney1, Marissa Giustina1, Rob Graff1,
Keith Guerin1, Steve Habegger1, Matthew P. Harrigan1, Michael J. Hartmann1,6, Alan Ho1,
Markus Hoffmann1, Trent Huang1, Travis S. Humble7, Sergei V. Isakov1, Evan Jeffrey1,
Zhang Jiang1, Dvir Kafri1, Kostyantyn Kechedzhi1, Julian Kelly1, Paul V. Klimov1, Sergey Knysh1,
Alexander Korotkov1,8, Fedor Kostritsa1, David Landhuis1, Mike Lindmark1, Erik Lucero1,
Dmitry Lyakh9, Salvatore Mandrà3,10 , Jarrod R. McClean1, Matthew McEwen5,
Anthony Megrant1, Xiao Mi1, Kristel Michielsen11,12 , Masoud Mohseni1, Josh Mutus1,
Ofer Naaman1, Matthew Neeley1, Charles Neill1, Murphy Yuezhen Niu1, Eric Ostby1,
Andre Petukhov1, John C. Platt1, Chris Quintana1, Eleanor G. Rieffel3, Pedram Roushan1,
Nicholas C. Rubin1, Daniel Sank1, Kevin J. Satzinger1, Vadim Smelyanskiy1, Kevin J. Sung1,13,
Matthew D. Trevithick1, Amit Vainsencher1, Benjamin Villalonga1,14 , Theodore White1,
Z. Jamie Yao1, Ping Yeh1, Adam Zalcman1, Hartmut Neven1 & John M. Martinis1,5*
The promise of quantum computers is that certain computational tasks might be
executed exponentially faster on a quantum processor than on a classical processor1. A
fundamental challenge is to build a high-delity processor capable of running quantum
algorithms in an exponentially large computational space. Here we report the use of a
processor with programmable superconducting qubits2–7 to create quantum states on
53 qubits, corresponding to a computational state-space of dimension 253 (about 1016).
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 supremacy8–14 for this specic computational task, heralding a much-
anticipated computing paradigm.
In the early 1980s, Richard Feynman proposed that a quantum computer
would be an effective tool with which to solve problems in physics
and chemistry, given that it is exponentially costly to simulate large
quantum systems with classical computers
1
. Realizing Feynman’s vision
poses substantial experimental and theoretical challenges. First, can
a quantum system be engineered to perform a computation in a large
enough computational (Hilbert) space and with a low enough error
rate to provide a quantum speedup? Second, can we formulate a prob-
lem that is hard for a classical computer but easy for a quantum com-
puter? By computing such a benchmark task on our superconducting
qubit processor, we tackle both questions. Our experiment achieves
quantum supremacy, a milestone on the path to full-scale quantum
computing8–14.
In reaching this milestone, we show that quantum speedup is achiev-
able in a real-world system and is not precluded by any hidden physical
laws. Quantum supremacy also heralds the era of noisy intermediate-
scale quantum (NISQ) technologies15. The benchmark task we demon-
strate has an immediate application in generating certifiable random
numbers (S. Aaronson, manuscript in preparation); other initial uses
for this new computational capability may include optimization16,17,
machine learning
18–21
, materials science and chemistry
22–24
. However,
realizing the full promise of quantum computing (using Shor’s algorithm
for factoring, for example) still requires technical leaps to engineer
fault-tolerant logical qubits25–29.
To achieve quantum supremacy, we made a number of techni-
cal advances which also pave the way towards error correction. We
https://doi.org/10.1038/s41586-019-1666-5
Received: 22 July 2019
Accepted: 20 September 2019
Published online: 23 October 2019
1Google AI Quantum, Mountain View, CA, USA. 2Department of Electrical and Computer Engineering, University of Massachusetts Amherst, Amherst, MA, USA. 3Quantum Artiicial Intelligence
Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA, USA. 4Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA. 5Department of Physics, University of
California, Santa Barbara, CA, USA. 6Friedrich-Alexander University Erlangen-Nürnberg (FAU), Department of Physics, Erlangen, Germany. 7Quantum Computing Institute, Oak Ridge National
Laboratory, Oak Ridge, TN, USA. 8Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA. 9Scientiic Computing, Oak Ridge Leadership Computing,
Oak Ridge National Laboratory, Oak Ridge, TN, USA. 10Stinger Ghaffarian Technologies Inc., Greenbelt, MD, USA. 11Institute for Advanced Simulation, Jülich Supercomputing Centre,
Forschungszentrum Jülich, Jülich, Germany. 12RWTH Aachen University, Aachen, Germany. 13Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor,
MI, USA. 14Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA. *e-mail: jmartinis@google.com
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Full-text available
  • Mar 2018
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.
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Tunable Coupling Scheme for Implementing High-Fidelity Two-Qubit Gates
Article
Full-text available
  • Mar 2018
The prospect of computational hardware with quantum advantage relies critically on the quality of quantum gate operations. Imperfect two-qubit gates is a major bottleneck for achieving scalable quantum information processors. Here, we propose a generalizable and extensible scheme for a two-qubit coupler switch that controls the qubit-qubit coupling by modulating the coupler frequency. Two-qubit gate operations can be implemented by operating the coupler in the dispersive regime, which is non-invasive to the qubit states. We investigate the performance of the scheme by simulating a universal two-qubit gate on a superconducting quantum circuit, and find that errors from known parasitic effects are strongly suppressed. The scheme is compatible with existing high-coherence hardware, thereby promising a higher gate fidelity with current technologies.
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Quantum-Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits
Article
  • Feb 2020
Quantum teleportation transfers and processes quantum information through quantum entanglement channels. It is one of the most versatile protocols in quantum information science and leads to many remarkable applications, particularly the one-way quantum computing. Here, we show, for the first time, that the concept of teleportation can also be used to facilitate an important classical computing task, sampling random quantum circuits, which is highly relevant to prove the near-term demonstration of quantum computational supremacy. In our method, the classical computation in the physical-qubit state space is converted to simulate teleportation in logical-qubit state space, resulting in a much smaller number of qubits involved in classical computing. We tested this new method on 1D and 2D lattices up to 1000 qubits. This Letter presents a new quantum-inspired classical computing technology and is helpful to design and optimize classically hard quantum sampling experiments.
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Fluctuations of Energy-Relaxation Times in Superconducting Qubits
Article
  • Aug 2018
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.
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