Topological qubits

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We don’t worry about errors in conventional computing chips because the digital transistor has hardware error correction built in. That’s why transistors replaced valves, unlocking the digital revolution. The idea behind topological qubits is to repeat this trick.

Topological qubit proponents often use the analogy of tying a knot in a piece of string. The point is that you can’t tell if a string is knotted by any single-point measurement. In the quantum world, this reduces the risk that any point disturbance forces the collapses of the qubit wave function into a purely knotted or un-knotted state.

We’ve long had an abstract model of how this could work, with common roots in the theory of topological error correcting codes . To make this work in hardware doesn’t require the discovery of new physics or new particles per se, but we do have to fabricate special nanostructures that we expect to behave as peculiar 1D or 2D quantum systems. The states required to make qubits are technically called non-Abelian anyons .

SWOT Analysis

Strengths

  • Error correction performed ‘in hardware’; potentially removing or significantly mitigating the large overhead required to implement quantum error correction ‘in software’.
  • Strong synergies with nanofabrication technology.

Opportunities

  • Majorana zero-modes in 1D nanowires offer one potential system on which topological qubits could be built .
  • Anyons have also recently been reported in a device using the fractional quantum Hall Effect .

Weaknesses

  • No working qubit platform has yet been demonstrated.
  • Extreme cryogenic cooling to mK temperatures is likely to be required.
  • Qubits are likely to be based on fabricated nanostructures and thus subject to variability.

Threats

  • This technology is starting a considerable distance behind other qubit approaches. If other ‘good enough’ technologies succeed first, they may establish a self-fulfilling lead in investment that is difficult to catch.

Key Players and Approaches

Notable commercial players: Microsoft/QuTech.

The overhead other qubit technologies will require to implement quantum error correction is expected to be massive. It is difficult to overstate the advantage any technology that significantly reduces this requirement will command. The history of conventional computing moving from valves to transistors provides a clear precedent for better fundamental hardware catching and replacing earlier tech.

A significant setback for this approach has been the recent  announcement that the 2018 Nature article announcing the unambiguous demonstration of Majorana zero-modes at TUDelft has had to be placed under review over doubts about how the raw data was processed and repeatability . Full details have yet to emerge. Fact Based Insight understands that the conclusions of earlier publications have not been called into question.

References

[1]
A. Y. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics, vol. 303, no. 1, pp. 2–30, 2003, doi: 10.1016/S0003-4916(02)00018-0. Available: http://arxiv.org/abs/quant-ph/9707021. [Accessed: Jul. 21, 2020]
[1]
H. Zhang et al., “Quantized Majorana conductance,” Nature, vol. 556, no. 7699, pp. 74–79, 2018, doi: 10.1038/nature26142. Available: http://arxiv.org/abs/1710.10701. [Accessed: Jul. 09, 2020]
[1]
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, “Non-Abelian Anyons and Topological Quantum Computation,” Rev. Mod. Phys., vol. 80, no. 3, pp. 1083–1159, Sep. 2008, doi: 10.1103/RevModPhys.80.1083. Available: http://arxiv.org/abs/0707.1889. [Accessed: Jul. 09, 2020]
[1]
“Expression of Concern about Quantized Majorana conductance publication,” QuTech, May 16, 2020. Available: https://qutech.nl/expression-of-concern-about-quantized-majorana-conductance-publication/. [Accessed: Jul. 09, 2020]
[1]
V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, “Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices,” Science, vol. 336, no. 6084, pp. 1003–1007, May 2012, doi: 10.1126/science.1222360. Available: http://arxiv.org/abs/1204.2792. [Accessed: Jul. 09, 2020]
[1]
J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, “Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state,” arXiv:2006.14115 [cond-mat], Jun. 2020, Available: http://arxiv.org/abs/2006.14115. [Accessed: Jul. 06, 2020]

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David Shaw

About the Author

David Shaw has worked extensively in consulting, market analysis & advisory businesses across a wide range of sectors including Technology, Healthcare, Energy and Financial Services. He has held a number of senior executive roles in public and private companies. David studied Physics at Balliol College, Oxford and has a PhD in Particle Physics from UCL. He is a member of the Institute of Physics. Follow David on Twitter and LinkedIn