Exponential suppression of bit or phase flip errors with repetitive quantum error correction
Michael Broughton
Masoud Mohseni
Andrew Dunsworth
Alan Ho
Matt Trevithick
Eric Ostby
Alan Derk
Rami Barends
Bálint Pató
Josh Mutus
Trevor Mccourt
Thomas E O'Brien
Sergei Isakov
Jamie Yao
Sean Harrington
Jeremy Patterson Hilton
Fedor Kostritsa
Trent Huang
Vladimir Shvarts
Nicholas Redd
Anthony Megrant
Charles Neill
Nicholas Bushnell
Wojtek Mruczkiewicz
Xiao Mi
Brooks Riley Foxen
Frank Carlton Arute
Marco Szalay
Orion Martin
Michael Newman
Alex Opremcak
William Courtney
Pavel Laptev
Vadim Smelyanskiy
Benjamin Chiaro
Jimmy Chen
Juan Atalaya
Daniel Eppens
Roberto Collins
Igor Aleiner
Yu Chen
Doug Strain
Dave Landhuis
Ping Yeh
Kunal Arya
Cody Jones
Edward Farhi
Andre Gregory Petukhov
Alexander Korotkov
Kostyantyn Kechedzhi
Alexandre Bourassa
Nature (2021)
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.
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