### A Breakthrough of Scalable Quantum Computing: First experimental demonstration of topological error correction

Yu-Ao Chen (left) and Jian-Wei Pan (right)

Scientists at the Division of Quantum Physics and Quantum Information (QPQI, Shanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China) -- in close collaboration with theoretical physicists from University of Melbourne (Australia) and University of British Columbia (Canada) -- have for the first time demonstrated topological error correction with eight-photon cluster state [1]. It represents an essential first step in that direction of building large-scale quantum computers.

Quantum computers have the potential to solve numerical problems that would be impossible on a classical computer. However quantum computing is very fragile. The imperfection of realistic physical devices inevitably introduces errors and destroys information. Fortunately, quantum error correction can be implemented, which enables quantum computers to tolerate an error rate per quantum bit (qubit) up to a threshold. For error rate below this threshold, quantum computing is efficiently possible and the results remain unaffected.

Topological error correction [2,3] is a quantum-error-correction scheme that makes use of topological properties in three dimensions [4] as well as active error correction method. The topological feature makes the quantum computing fault-robust: many errors on physical devices won't be “seen” by logical qubits and do not affect computing results. Moreover, while performing quantum computing, one can actively analyzes the syndromes from measurements and monitors whether and what errors occur. If so, error correction is immediately implemented.

In comparison with conventional error correction in quantum computing, topological error correction has the highest known tolerable error rate 0.7-1.1% (for the traditional error correction codes the highest threshold is 2.2×10

^{-5}), and is more friendly to realistic physical devices that are imperfect and unavoidably suffer from errors. Moreover, the architecture used in topological error correction is rather simple: it is sufficient to create interactions between two qubits that are neighbors of each other. Thus, topological error correction can increase the tolerance for experimental errors to the point that it is consistent with experimental capabilities. This greatly increases the prospects for building large-scale quantum computers. The experiment [1] provides a proof of principle that topological error correction would be one of the most practical approaches for designing quantum computers.

Figure 1 (a) The structure of the prepared eight photon cluster state and the topological feature. (b) The experimental setup for the eight photon cluster state.

In the experiment, physicists have designed an eight photon cluster state (See Fig. 1a) to achieve the topological error correction. Based on a newly developed ultrabright entangled-photon source by using an interferometric Bell-type synthesizer and a noise-reduction interferometer [5] that utilizes spontaneous parametric down-conversion and linear optics, the desired eight-photon cluster state is created with high fidelity (See Fig. 1b). Then each qubit is measured locally. Error syndromes are constructed from the measurement outcomes, and it is shown that a correlation can be protected against a single error on any qubit. If only one physical qubit suffers an error, the faulty qubit can be located and corrected, and that if all qubits are simultaneously subjected to errors with equal probability, the effective error rate is significantly reduced by error correction. This constitutes a proof-of-principle experiment that demonstrates the viability of topological error correction, a central ingredient in topological cluster-state computing.

Figure 2: Artist’s view showing the working principle of topological cluster-state quantum computing. Each lantern resembles the topological structure of the eight-photon cluster state which realizes one topologically protected qubit.

Figure 3: Set-up for topological error correction.

The demonstration of topological error correction is a breakthrough step towards scalable fault-tolerant quantum computation. The high threshold error rate is especially remarkable given that only nearest-neighbor interactions are required. Owing to these advantages, topological error correction is especially well suited for physical systems that are geometrically constrained to nearest-neighbor interactions, such as quantum dots, Josephson junction, ion traps, cold atoms in optical lattices and photonic modules.

Reference

[1] X.-C. Yao, T.-X. Wang, H.-Z. Chen, W.-B. Gao, A. G. Fowler, R. Raussendorf, Z.-B. Chen, N.-L. Liu, C.-Y. Lu, Y.-J. Deng, Y.-A. Chen & J.-W. Pan, “Experimental demonstration of topological error correction” , Nature 482, 489 (2012). Abstract.

[2] R. Raussendorf, & J. Harrington, “Fault-tolerant quantum computation with high threshold in two dimensions”, Phys. Rev. Lett. 98, 190504 (2007). Abstract.

[3] D. S. Wang, A. G. Austin, & L. C. L. Hollenberg, “Quantum computing with nearest neighbor interactions and error rates over 1%”, Phys. Rev. A 83, 020302(R) (2011). Abstract.

[4] C. Nayak, S. H. Simon, A. Stern, M. Freedman, & S. Das Sarma, “Non-Abelian anyons and topological quantum computation”, Rev. Mod. Phys. 80, 1083–1159 (2008). Abstract.

[5] X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, J.-W. Pan, “Observation of eight-photon entanglement”, Nature Photonics, doi:10.1038/nphoton.2011.354 (published online February 12, 2012). Abstract.

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