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Exponential suppression of bit or phase errors with cyclic error correction
Nature ( IF 64.8 ) Pub Date : 2021-07-14 , DOI: 10.1038/s41586-021-03588-y
Zijun Chen 1 , Kevin J. Satzinger 1 , Juan Atalaya 1 , Alexander N. Korotkov 1, 2 , Andrew Dunsworth 1 , Daniel Sank 1 , Chris Quintana 1 , Matt McEwen 1, 3 , Rami Barends 1 , Paul V. Klimov 1 , Sabrina Hong 1 , Cody Jones 1 , Andre Petukhov 1 , Dvir Kafri 1 , Sean Demura 1 , Brian Burkett 1 , Craig Gidney 1 , Austin G. Fowler 1 , Harald Putterman 1 , Igor Aleiner 1 , Frank Arute 1 , Kunal Arya 1 , Ryan Babbush 1 , Joseph C. Bardin 1, 4 , Andreas Bengtsson 1 , Alexandre Bourassa 1, 5 , Michael Broughton 1 , Bob B. Buckley 1 , David A. Buell 1 , Nicholas Bushnell 1 , Benjamin Chiaro 1 , Roberto Collins 1 , William Courtney 1 , Alan R. Derk 1 , Daniel Eppens 1 , Catherine Erickson 1 , Edward Farhi 1 , Brooks Foxen 1 , Marissa Giustina 1 , Ami Greene 1, 6 , Jonathan A. Gross 1 , Matthew P. Harrigan 1 , Sean D. Harrington 1 , Jeremy Hilton 1 , Alan Ho 1 , Trent Huang 1 , William J. Huggins 1 , L. B. Ioffe 1 , Sergei V. Isakov 1 , Evan Jeffrey 1 , Zhang Jiang 1 , Kostyantyn Kechedzhi 1 , Seon Kim 1 , Alexei Kitaev 1, 7 , Fedor Kostritsa 1 , David Landhuis 1 , Pavel Laptev 1 , Erik Lucero 1 , Orion Martin 1 , Jarrod R. McClean 1 , Trevor McCourt 1 , Xiao Mi 1 , Kevin C. Miao 1 , Masoud Mohseni 1 , Shirin Montazeri 1 , Wojciech Mruczkiewicz 1 , Josh Mutus 1 , Ofer Naaman 1 , Matthew Neeley 1 , Charles Neill 1 , Michael Newman 1 , Murphy Yuezhen Niu 1 , Thomas E. O’Brien 1 , Alex Opremcak 1 , Eric Ostby 1 , Bálint Pató 1 , Nicholas Redd 1 , Pedram Roushan 1 , Nicholas C. Rubin 1 , Vladimir Shvarts 1 , Doug Strain 1 , Marco Szalay 1 , Matthew D. Trevithick 1 , Benjamin Villalonga 1 , Theodore White 1 , Z. Jamie Yao 1 , Ping Yeh 1 , Juhwan Yoo 1 , Adam Zalcman 1 , Hartmut Neven 1 , Sergio Boixo 1 , Vadim Smelyanskiy 1 , Yu Chen 1 , Anthony Megrant 1 , Julian Kelly 1 , Alexandru Paler 8, 9
Affiliation  

Realizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2,3,4,5,6,7,8,9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10,11,12,13,14). Quantum error correction15,16,17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold 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 analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.



中文翻译:

通过循环纠错以指数方式抑制位或相位错误

实现量子计算的潜力需要足够低的逻辑错误率1。许多应用要求错误率低至 10 -15(参考文献2、3、4、5、6、7、8、9),但最先进的量子平台通常具有接近 10 的物理错误率- 3(参考文献10、11、12、13、14)。量子纠错15,16,17承诺通过在许多物理量子位上分布量子逻辑信息来弥合这一鸿沟,从而可以检测和纠正错误。如果物理错误率低于某个阈值并且在计算过程中保持稳定,则编码逻辑量子位状态上的错误可以随着物理量子位数量的增长而以指数方式抑制。在这里,我们实现了嵌入在二维超导量子比特网格中的一维重复码,该代码展示了比特翻转或相位翻转误差的指数抑制,当量子比特数从 5 个增加时,每轮逻辑错误减少 100 倍以上到 21. 至关重要的是,这种错误抑制在 50 轮纠错之后是稳定的。我们还介绍了一种高精度分析误差相关性的方法,允许我们在执行量子纠错时表征错误局部性。最后,我们在同一设备上使用 2D 表面码使用小的逻辑量子位执行错误检测18,19并表明一维和二维码的结果与使用简单去极化误差模型的数值模拟一致。这些实验演示为构建具有超导量子位的可扩展容错量子计算机提供了基础。

更新日期:2021-07-14
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