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Realization of three-qubit quantum error correction with superconducting circuits

Abstract

Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes1. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used2. Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state3,4, induce errors on the qubits and decode the error syndrome—a quantum state indicating which error has occurred—by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 ± 1 per cent fidelity to the expected classical action of this gate, and 78 ± 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times5,6, this could lead to scalable quantum technology.

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Figure 1: Calculated energy spectra and time-domain measurements of the interactions used in the three-qubit gate.
Figure 2: Pulse sequence and classical action of the three-qubit gate.
Figure 3: Bit-flip error correction demonstrating recovery from a single arbitrary rotation.
Figure 4: Demonstration of first-order insensitivity to simultaneous phase-flip errors.

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Acknowledgements

We thank G. Kirchmair, M. Mirrahimi, I. Chuang and M. Devoret for discussions. We acknowledge support from LPS/NSA under ARO contract no. W911NF-09-1-0514 and from the NSF under grants no. DMR-0653377 and no. DMR-1004406. Additional support was provided by CNR-Istituto di Cibernetica, Pozzuoli, Italy (L.F.), the Swiss NSF (S.E.N.) and the Dutch NWO (L.D.C.).

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Contributions

M.D.R. carried out measurements and performed data analysis. L.D.C. designed the three-qubit gate and conducted initial measurements. L.S. provided further experimental contributions. S.E.N. and S.M.G. provided theoretical support. L.F., L.D.C. and L.S. fabricated the devices. M.D.R. wrote the manuscript, with feedback from all authors. S.M.G. and R.J.S. designed and supervised the project.

Corresponding authors

Correspondence to M. D. Reed or R. J. Schoelkopf.

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The authors declare no competing financial interests.

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Reed, M., DiCarlo, L., Nigg, S. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012). https://doi.org/10.1038/nature10786

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