Abstract
The hopes for scalable quantum computing rely on the “threshold theorem”: once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based on a number of assumptions, which are supposed to be satisfied exactly, like axioms, e.g., zero undesired interactions between qubits, etc. However, in the physical world no continuous quantity can be exactly zero, it can only be more or less small. Thus the “error per qubit per gate” threshold must be complemented by the required precision with which each assumption should be fulfilled. In the absence of this crucial information, the prospects of scalable quantum computing remain uncertain.
Similar content being viewed by others
References
A. Steane, Rep. Prog. Phys. 61, 117 (1998); arXiv:quant-ph/9708022.
Report of the Quantum Information Science and Technology Experts Panel. http://qist.lanl.gov/qcomp-map.shtml
P. Shor, in Proceedings of the 37th Symposium on Foundations of Computing (IEEE Computer Society Press, 1996), p. 56; arXiv:quant-ph/9605011.
J. Preskill, in Introduction to Quantum Computation and Information, Ed. by H.-K. Lo, S. Papesku, and T. Spiller (World Scientific, Singapore, 1998), p. 213; arXiv:quant-ph/9712048.
D. Gottesman, in Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, Ed. by S. J. Lomonaco, Jr. (American Mathematical Society, Providence, Rhode Island, 2002), p. 221; arXiv:quant-ph/0004072.
A. M. Steane, in Decoherence and Its Implications in Quantum Computation and Information Transfer, Ed. by A. Gonis and P. Turchi (IOS Press, Amsterdam, 2001), p. 284; arXiv:quant-ph/0304016.
A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996).
A. M. Steane, Phys. Rev. Lett. 77, 793 (1996).
D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on the Theory of Computation (ACM Press, New York, 1998), p. 176; arXiv:quant-ph/9611025; arXiv:quant-ph/9906129.
A. Yu. Kitaev, Russ. Math. Surv. 52, 1191 (1997); A. Yu. Kitaev, in Quantum Communication, Computing, and Measurement, Ed. by O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997), p. 181.
E. Knill, R. Laflamme, and W. Zurek, Proc. R. Soc. London A 454, 365 (1998); arXiv: quant-ph/9702058.
P. Aliferis, D. Gottesman, and J. Preskill, Quantum Inf. Comput. 8, 181 (2008); arXiv:quant-ph/0703264.
E. Knill, Nature 463, 441 (2010).
D. Staudt, arXiv:1111.1417 (2011).
J. Preskill, Proc. R. Soc. London A 454, 469 (1998); arXiv:quant-ph/9705032.
J. Preskill, in Introduction to Quantum Computation, Ed. by H.-K. Lo, S. Popescu, and T. P. Spiller (World Scientific, Singapore, 1998); arXiv:quant-ph/9712048.
M. I. Dyakonov, in Future Trends in Microelectronics. Up the Nano Creek, Ed. by S. Luryi, J. Xu, and A. Zaslavsky (Wiley, New York, 2007), p. 4; arXiv:quant-ph/0610117.
M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
P. Schindler et al., Science 332, 1059 (2011); E. Lucero et al., arXiv:1202.5707 (2012); M. D. Reed et al., Nature 482, 382 (2012); Xing-Can Yao et al., arXiv:1202.5459 (2012); E. Martín-López et al., Nature Photon. 6, 773 (2012); arXiv:1111.4147 (2011).
J. Preskill, Quantum Inf. Comput. 13, 181 (2013); arXiv:1207.6131 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Dyakonov, M.I. Revisiting the hopes for scalable quantum computation. Jetp Lett. 98, 514–518 (2013). https://doi.org/10.1134/S0021364013210042
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364013210042