Experimental demonstration of topological error correction

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Scalable quantum computing can be achieved only if quantum bits are manipulated in a fault-tolerant fashion. Topological error correction—a method that combines topological quantum computation with quantum error correction—has the highest known tolerable error rate for a local architecture. The technique makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the experimental demonstration of topological error correction with an eight-photon cluster state. We show that a correlation can be protected against a single error on any quantum bit. Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing.

At a glance


  1. Topological cluster states.
    Figure 1: Topological cluster states.

    a, Elementary lattice cell. Dashed lines represent the edges of the associated cell complex and solid lines represent the edges of the interaction graph. Qubits (spheres) are encoded on the faces and edges of the elementary cell. b, Larger topological cluster state of 5×5×T cells. Green dots represent local Z measurements, which effectively remove the measured qubits from the cluster state and thereby create a non-trivial topology capable of supporting a single correlation. Red dots represent Z errors. Red cells indicate the ends of error chains where CF = −1. One axis of the cluster can be regarded as simulating the ‘circuit time’, t. The evolution of logical states from t1 to t2 is achieved by performing local X measurements on all physical qubits between t1 and t2.

  2. Cluster state |G8> and its cell complex.
    Figure 2: Cluster state |G8> and its cell complex.

    a, G8, the interaction graph of |G8right fence. b, The corresponding 3D cell complex, with volumes {v, w, y, z}, faces {f1, f2, f3, f4, f5, f6}, edges {e7, e8} and vertices {s, t}. The exterior and the centre volume are not in the complex. For better illustration, the cell complex is cut open and the foreground quarter is removed (silhouette view from right is shown for clarity).

  3. Experimental set-up for the generation of the eight-photon cluster state and the demonstration of topological error correction.
    Figure 3: Experimental set-up for the generation of the eight-photon cluster state and the demonstration of topological error correction.

    a, Creation of ultrabright entangled-photon pairs. An ultraviolet laser pulse passes through a 2-mm, nonlinear β-barium borate crystal, creating an entangled photon pair {a, b} with density matrix by parametric down-conversion, where o and e indicate ordinary and extraordinary polarizations, respectively perpendicular and parallel relative to the V-polarized pump. After both photons pass through compensators, which include a 45° half-wave plate (HWP) and a 1-mm β-barium borate crystal, one of the photons’ polarizations is rotated by another 45° HWP. Then we re-overlap the two photons on a PBS, creating an entangled photon pair in a state , where |earight fence is a state in which all photons in path a have extraordinary polarization and |obright fence is a state in which all photons in path b have ordinary polarization. b, To create the desired cluster state, we combine photons from paths 6 and 8 at the first PDBS and let each photon pass through another PDBS (PDBS′), resulting a controlled-phase operation between the two photons. At the same time, photons 2 and 4 are interfered on PBS1. Then photons 4′ and 6′ are overlapped on PBS2. On coincidence detection, we create the eight-photon cluster state (equation (3)) for topological error correction. c, Polarization analyser for each individual photon, containing a quarter-wave plate (QWP), a HWP, a PBS and two single-mode, fibre-coupled single-photon detectors.

  4. Experimental results for the created eight-photon cluster state.
    Figure 4: Experimental results for the created eight-photon cluster state.

    a, Measured eightfold coincidence in the {|Hright fence, |V} basis. b, The expectation values for different witness measurement settings. The measurement settings are and with i = 0, ..., 5. The measurement of each setting takes 50h for the first two settings and 30h for the remaining settings. c, Correlations for the initial state without any simulated error. Error bars, 1s.d., deduced from propagated Poissonian counting statistics of the raw detection events.

  5. Experimental results of syndrome correlations for topological error correction.
    Figure 5: Experimental results of syndrome correlations for topological error correction.

    Only one qubit is subjected to an X error in each plot. The measurement for each error setting takes about 80h. Error bars, 1s.d., deduced from propagated Poissonian counting statistics of the raw detection events.

  6. Experimental results of topological error correction.
    Figure 6: Experimental results of topological error correction.

    All physical qubits are simultaneously subject to an X error with equal probability ranging from 0 to 1. The blue circles and blue lines represent the experimental and, respectively, theoretical values of the error rate for the protected correlation without TEC, and the red squares and red lines similarly represent the error rate with TEC. The agreement between the experimental and the theoretical results demonstrates the viability of TEC. The measurement of each data point takes 80h. Error bars, 1s.d., deduced from propagated Poissonian counting statistics of the raw detection events.


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Author information


  1. Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China

    • Xing-Can Yao,
    • Tian-Xiong Wang,
    • Hao-Ze Chen,
    • Wei-Bo Gao,
    • Zeng-Bing Chen,
    • Nai-Le Liu,
    • Chao-Yang Lu,
    • You-Jin Deng,
    • Yu-Ao Chen &
    • Jian-Wei Pan
  2. CQC2T, School of Physics, University of Melbourne, Victoria 3010, Australia

    • Austin G. Fowler
  3. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada

    • Robert Raussendorf


W.-B.G., A.G.F., R.R., Z.-B.C., Y.-J.D. and J.-W.P. had the idea for and initiated the experiment. A.G.F., R.R. and Y.-J.D. contributed to the general theoretical work. X.-C.Y., C.-Y.L., Y.-A.C. and J.-W.P. designed the experiment. X.-C.Y., T.-X.W. and H.-Z.C. carried out the experiment. X.-C.Y. and Y.-A.C. analysed the data. X.-C.Y., A.G.F., R.R., N.-L.L., C.-Y.L., Y.-J.D., Y.-A.C. and J.-W.P. wrote the manuscript. N.-L.L., Y.-A.C. and J.-W.P. supervised the whole project.

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