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Nature | Vol 574 | 24 OCTOBER 2019 | 505

Article

Quantum supremacy using a programmable

superconducting processor

Frank Arute

, Kunal Arya

, Ryan Babbush

, Dave Bacon

, Joseph C. Bardin

1,2

, Rami Barends

Rupak Biswas

, Sergio Boixo

, Fernando G. S. L. Brandao

1,4

, David A. Buell

, Brian Burkett

Yu Chen

, Zijun Chen

, Ben Chiaro

, Roberto Collins

, William Courtney

, Andrew Dunsworth

Edward Farhi

, Brooks Foxen

1,5

, Austin Fowler

, Craig Gidney

, Marissa Giustina

, Rob Graff

Keith Guerin

, Steve Habegger

, Matthew P. Harrigan

, Michael J. Hartmann

1,6

, Alan Ho

Markus Hoffmann

, Trent Huang

, Travis S. Humble

, Sergei V. Isakov

, Evan Jeffrey

Zhang Jiang

, Dvir Kafri

, Kostyantyn Kechedzhi

, Julian Kelly

, Paul V. Klimov

, Sergey Knysh

Alexander Korotkov

1,8

, Fedor Kostritsa

, David Landhuis

, Mike Lindmark

, Erik Lucero

Dmitry Lyakh

, Salvatore Mandrà

3,10

, Jarrod R. McClean

, Matthew McEwen

Anthony Megrant

, Xiao Mi

, Kristel Michielsen

11,12

, Masoud Mohseni

, Josh Mutus

Ofer Naaman

, Matthew Neeley

, Charles Neill

, Murphy Yuezhen Niu

, Eric Ostby

Andre Petukhov

, John C. Platt

, Chris Quintana

, Eleanor G. Rieffel

, Pedram Roushan

Nicholas C. Rubin

, Daniel Sank

, Kevin J. Satzinger

, Vadim Smelyanskiy

, Kevin J. Sung

1,13

Matthew D. Trevithick

, Amit Vainsencher

, Benjamin Villalonga

1,14

, Theodore White

Z. Jamie Yao

, Ping Yeh

, Adam Zalcman

, Hartmut Neven

& John M. Martinis

1,5

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-delity processor capable of running quantum

algorithms in an exponentially large computational space. Here we report the use of a

processor with programmable superconducting qubits

2–7

to create quantum states on

53 qubits, corresponding to a computational state-space of dimension 2

(about 10

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

8–14

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

. 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

computing

8–14

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) technologies

. 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 optimization

16,17

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 qubits

25–29

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

Google AI Quantum, Mountain View, CA, USA.

Department of Electrical and Computer Engineering, University of Massachusetts Amherst, Amherst, MA, USA.

Quantum Artiicial Intelligence

Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA, USA.

Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA.

Department of Physics, University of

California, Santa Barbara, CA, USA.

Friedrich-Alexander University Erlangen-Nürnberg (FAU), Department of Physics, Erlangen, Germany.

Quantum Computing Institute, Oak Ridge National

Laboratory, Oak Ridge, TN, USA.

Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA.

Scientiic Computing, Oak Ridge Leadership Computing,

Oak Ridge National Laboratory, Oak Ridge, TN, USA.

Stinger Ghaffarian Technologies Inc., Greenbelt, MD, USA.

Institute for Advanced Simulation, Jülich Supercomputing Centre,

Forschungszentrum Jülich, Jülich, Germany.

RWTH Aachen University, Aachen, Germany.

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor,

MI, USA.

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA. *e-mail: jmartinis@google.com

506 | Nature | Vol 574 | 24 OCTOBER 2019

Article

developed fast, high-fidelity gates that can be executed simultaneously

across a two-dimensional qubit array. We calibrated and benchmarked

the processor at both the component and system level using a powerful

new tool: cross-entropy benchmarking

. Finally, we used component-

level fidelities to accurately predict the performance of the whole sys-

tem, further showing that quantum information behaves as expected

when scaling to large systems.

A suitable computational task

To demonstrate quantum supremacy, we compare our quantum proces-

sor against state-of-the-art classical computers in the task of sampling

the output of a pseudo-random quantum circuit

11,13,14

. Random circuits

are a suitable choice for benchmarking because they do not possess

structure and therefore allow for limited guarantees of computational

hardness

10–12

. We design the circuits to entangle a set of quantum bits

(qubits) by repeated application of single-qubit and two-qubit logi-

cal operations. Sampling the quantum circuit’s output produces a set

of bitstrings, for example {0000101, 1011100, …}. Owing to quantum

interference, the probability distribution of the bitstrings resembles

a speckled intensity pattern produced by light interference in laser

scatter, such that some bitstrings are much more likely to occur than

others. Classically computing this probability distribution becomes

exponentially more difficult as the number of qubits (width) and number

of gate cycles (depth) grow.

We verify that the quantum processor is working properly using a

method called cross-entropy benchmarking

11,12,14

, which compares how

often each bitstring is observed experimentally with its corresponding

ideal probability computed via simulation on a classical computer. For

a given circuit, we collect the measured bitstrings {x

} and compute the

linear cross-entropy benchmarking fidelity

11,13,14

(see alsoSupplementary

Information), which is the mean of the simulated probabilities of the

bitstrings we measured:

Px=2 ⟨()⟩ −1

)

XEB

where n is the number of qubits, P(x

) is the probability of bitstring x

computed for the ideal quantum circuit, and the average is over the

observed bitstrings. Intuitively,

XEB

is correlated with how often we

sample high-probability bitstrings. When there are no errors in the

quantum circuit, the distribution of probabilities is exponential (see

Supplementary Information), and sampling from thisdistribution will

produce

F =1

XEB

. On the other hand, sampling from the uniform

distribution will give ⟨P(x

)⟩

=1/2

and produce

F =0

XEB

. Values of

XEB

between 0 and 1 correspond to the probability that no error has occurred

while running the circuit. The probabilities P(x

) must be obtained from

classically simulating the quantum circuit, and thus computing

XEB

intractable in the regime of quantum supremacy. However, with certain

circuit simplifications, we can obtain quantitative fidelity estimates of

a fully operating processor running wide and deep quantum circuits.

Our goal is to achieve a high enough

XEB

for a circuit with sufficient

width and depth such that the classical computing cost is prohibitively

large. This is a difficult task because our logic gates are imperfect and

the quantum states we intend to create are sensitive to errors. A single

bit or phase flip over the course of the algorithm will completely shuffle

the speckle pattern and result in close to zero fidelity

(see alsoSup-

plementary Information). Therefore, in order to claim quantum suprem-

acy we need a quantum processor that executes the program with

sufficiently low error rates.

Building a high-fidelity processor

We designed a quantum processor named ‘Sycamore’ which consists

of a two-dimensional array of 54 transmon qubits, where each qubit is

tunably coupled to four nearest neighbours, in a rectangular lattice. The

connectivity was chosen to be forward-compatible with error correc-

tion using the surface code

. A key systems engineering advance of this

device is achieving high-fidelity single- and two-qubit operations, not

just in isolation but also while performing a realistic computation with

simultaneous gate operations on many qubits. We discuss the highlights

below; see also theSupplementary Information.

In a superconducting circuit, conduction electrons condense into a

macroscopic quantum state, such that currents and voltages behave

quantum mechanically

2,30

. Our processor uses transmon qubits

, which

can be thought of as nonlinear superconducting resonators at 5–7GHz.

The qubit is encoded as the two lowest quantum eigenstates of the

resonant circuit. Each transmon has two controls: a microwave drive

to excite the qubit, and a magnetic flux control to tune the frequency.

Each qubit is connected to a linear resonator used to read out the qubit

state

. As shown in Fig.1, each qubit is also connected to its neighbouring

qubits using a new adjustable coupler

31,32

. Our coupler design allows us

to quickly tune the qubit–qubit coupling from completely off to 40MHz.

One qubit did not function properly, so the device uses 53 qubits and

86 couplers.

The processor is fabricated using aluminium for metallization and

Josephson junctions, and indium for bump-bonds between two silicon

wafers. The chip is wire-bonded to a superconducting circuit board

and cooled to below 20mK in a dilution refrigerator to reduce ambient

thermal energy to well below the qubit energy. The processor is con-

nected through filters and attenuators to room-temperature electronics,

Qubit

Adjustable coupler

10 mm

Fig. 1 | 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.

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