Extending the lifetime of a quantum bit with error correction in superconducting circuits

Abstract

Quantum error correction (QEC) can overcome the errors experienced by qubits1 and is therefore an essential component of a future quantum computer. To implement QEC, a qubit is redundantly encoded in a higher-dimensional space using quantum states with carefully tailored symmetry properties. Projective measurements of these parity-type observables provide error syndrome information, with which errors can be corrected via simple operations2. The ‘break-even’ point of QEC—at which the lifetime of a qubit exceeds the lifetime of the constituents of the system—has so far remained out of reach3. Although previous works have demonstrated elements of QEC4,5,6,7,8,9,10,11,12,13,14,15,16, they primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to preserve a qubit over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of Schrödinger-cat states17 of a superconducting resonator18,19,20,21. We implement a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode and correct. As measured by full process tomography, without any post-selection, the corrected qubit lifetime is 320 microseconds, which is longer than the lifetime of any of the parts of the system: 20 times longer than the lifetime of the transmon, about 2.2 times longer than the lifetime of an uncorrected logical encoding and about 1.1 longer than the lifetime of the best physical qubit (the |0〉f and |1〉f Fock states of the resonator). Our results illustrate the benefit of using hardware-efficient qubit encodings rather than traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming basic concepts to exploring the metrics that drive system performance and the challenges in realizing a fault-tolerant system.

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Figure 1: The cat-code cycle.
Figure 2: Example of a two-step quantum trajectory executed by the QEC state machine.
Figure 3: QEC process tomography.

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Acknowledgements

We thank K. Sliwa, A. Narla and L. Sun for discussions. This research was supported by the US Army Research Office (W911NF-14-1-0011). A.P. was supported by the National Science Foundation (NSF) (PHY-1309996). S.M.G. acknowledges additional support from NSF DMR-1301798. Facilities use was supported by the Yale Institute for Nanoscience and Quantum Engineering (YINQE), the Yale SEAS cleanroom and the NSF (MRSECDMR 1119826).

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Contributions

A.P. and N.O. performed the experiment and analysed the data. N.O. designed and built the feedback architecture with help from Y.L. under the supervision of R.J.S. and M.H.D. R.H. and P.R. developed the optimal control pulses. M.M., Z.L., L.J., S.M.G. and B.V. provided theoretical support. R.H. and L.F. fabricated the transmon qubit. R.J.S. supervised the project. A.P., N.O., L.F. and R.J.S. wrote the manuscript with feedback from all authors.

Corresponding authors

Correspondence to Nissim Ofek or Andrei Petrenko or R. J. Schoelkopf.

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Competing interests

R.J.S., M.H.D. and L.F. are founders and equity shareholders of Quantum Circuits, Inc.

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This file contains Supplementary Text and Data including Supplementary Methods, additional references, Supplementary Tables 1-2 and Supplementary Figures 1-11. (PDF 7058 kb)

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Ofek, N., Petrenko, A., Heeres, R. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016). https://doi.org/10.1038/nature18949

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