A robust W-state encoding for linear quantum optics

Madhav Krishnan Vijayan1, Austin P. Lund2, and Peter P. Rohde1

1Centre for Quantum Software & Information (UTS:QSI), University of Technology Sydney, Sydney NSW, Australia
2Centre for Quantum Computation & Communications Technology, School of Mathematics & Physics, The University of Queensland, St Lucia QLD, Australia

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest in $\textit{passive}$ linear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems are $\textit{passive}$ by definition. In usual scenarios, error detection and correction techniques are inherently $\textit{active}$, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit. We present our scheme in the context of a single photonic qubit passing through a noisy communication or quantum memory channel, which has not been generalised to the more general context of full quantum computation.

► BibTeX data

► References

[1] Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. In Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing, STOC '11, page 333, 2011. 10.1364/​qim.2014.qth1a.2.

[2] Scott Aaronson and Alex Arkhipov. Bosonsampling is far from uniform. Quantum Information and Computation, 14: 1383, 2014.

[3] Scott Aaronson and Daniel J. Brod. BosonSampling with lost photons. Physical Review A, 93, 2016. 10.1103/​physreva.93.012335.

[4] Alex Arkhipov. BosonSampling is robust against small errors in the network matrix. Physical Review A, 92, 2015. 10.1103/​physreva.92.062326.

[5] Michael J. Bremner, Richard Jozsa, and Dan J. Shepherd. Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467: 459, 2011. 10.1098/​rspa.2010.0301.

[6] Daniel E. Browne, Jens Eisert, Stefan Scheel, and Martin B. Plenio. Driving non-gaussian to gaussian states with linear optics. Physical Review A, 67, 2003. 10.1103/​physreva.67.062320.

[7] L-M Duan, Mikhail D. Lukin, J. Ignacio Cirac, and Peter Zoller. Long-distance quantum communication with atomic ensembles and linear optics. Nature, 414: 413, 2001. 10.1038/​35106500.

[8] Wolfgang Dür, Guifre Vidal, and J. Ignacio Cirac. Three qubits can be entangled in two inequivalent ways. Physical Review A, 62: 062314, 2000. 10.1103/​physreva.62.062314.

[9] Jens Eisert, Stefan Scheel, and Martin B. Plenio. Distilling gaussian states with gaussian operations is impossible. Physical Review Letters, 89: 137903, 2002. 10.1103/​physrevlett.89.137903.

[10] Fabian Ewert and Peter van Loock. Ultrafast fault-tolerant long-distance quantum communication with static linear optics. Phys. Rev. A, 95: 012327, Jan 2017. 10.1103/​PhysRevA.95.012327.

[11] Nicolas Gisin, Noah Linden, Serge Massar, and S Popescu. Error filtration and entanglement purification for quantum communication. Physical Review A, 72: 012338, 2005. 10.1103/​physreva.72.012338.

[12] Aram W. Harrow and Ashley Montanaro. Quantum computational supremacy. Nature, 549: 203, 2017. 10.1038/​nature23458.

[13] YuXiao Jiang, PengLiang Guo, ChengYan Gao, HaiBo Wang, Faris Alzahrani, Aatef Hobiny, and FuGuo Deng. Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements. Science China Physics, Mechanics & Astronomy, 60: 120312, 2017. 10.1007/​s11433-017-9091-0.

[14] Gil Kalai and Guy Kindler. Gaussian Noise Sensitivity and BosonSampling, 2014. https:/​/​arxiv.org/​abs/​1409.3093.

[15] Emanuel Knill, Raymond Laflamme, and Gerald Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409: 46, 2001. 10.1038/​35051009.

[16] Anthony Leverrier and Raúl García-Patrón. Analysis of circuit imperfections in bosonsampling. Quantum Information and Computation, 15: 489, 2015. ISSN 1533.

[17] Xi-Han Li, Fu-Guo Deng, and Hong-Yu Zhou. Faithful qubit transmission against collective noise without ancillary qubits. Applied Physics Letters, 91: 144101, 2007. 10.1063/​1.2794433.

[18] Austin P. Lund, Michael J. Bremner, and Timothy C. Ralph. Quantum sampling problems, bosonsampling and quantum supremacy. NPJ Quantum Information, 3: 15, 2017. 10.1038/​s41534-017-0018-2.

[19] Ryan J. Marshman, Austin P. Lund, Peter P. Rohde, and Timothy Cameron Ralph. Passive quantum error correction of linear optics networks through error averaging. Physical Review A, 97: 22324, 2018. 10.1103/​PhysRevA.97.022324.

[20] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000. 10.1017/​cbo9780511976667.

[21] John Preskill. Fault-Tolerant Quantum Computation, chapter 8, page 213. World Scientific, 1998. 10.1142/​9789812385253_0008.

[22] Saleh Rahimi-Keshari, Timothy C. Ralph, and Carlton M. Caves. Sufficient conditions for efficient classical simulation of quantum optics. Physical Review X, 6: 21039, 2016. 10.1103/​PhysRevX.6.021039.

[23] Timothy C. Ralph and Austin P. Lund. Nondeterministic noiseless linear amplification of quantum systems. In AIP Conference Proceedings. AIP, 2009. 10.1063/​1.3131295.

[24] R. Raussendorf and H. J. Briegel. A one-way quantum computer. Physical Review Letters, 86: 5188, 2001. 10.1103/​physrevlett.86.5188.

[25] R. Raussendorf, D. E. Browne, and H. J. Briegel. Measurement-based quantum computation on cluster states. Physical Review A, 68: 022312, 2003. 10.1103/​physreva.68.022312.

[26] Peter P. Rohde and Timothy C. Ralph. Error models for mode-mismatch in linear optics quantum computing. Physical Review A, 73: 062312, 2006. 10.1103/​physreva.73.062312.

[27] Peter P. Rohde and Timothy C. Ralph. Error tolerance of the boson-sampling model for linear optics quantum computing. Physical Review A, 85: 022332, 2012. 10.1103/​physreva.85.022332.

[28] V. S. Shchesnovich. Sufficient condition for the mode mismatch of single photons for scalability of the boson-sampling computer. Physical Review A, 89, 2014. 10.1103/​PhysRevA.89.022333.

[29] Dan Shepherd and Michael J. Bremner. Temporally unstructured quantum computation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465: 1413, 2009. 10.1098/​rspa.2008.0443.

[30] Peter W. Shor. Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52: R2493, 1995. 10.1103/​physreva.52.r2493.

[31] Peter W. Shor. Fault-tolerant quantum computation. In 37th Symposium on Foundations of Computing, page 56. IEEE Computer Society Press, 1996. 10.1007/​978-1-4939-2864-4_143.

[32] Malte C. Tichy. Sampling of partially distinguishable bosons and the relation to the multidimensional permanent. Physical Review A, 91, 2015. 10.1103/​PhysRevA.91.022316.

[33] Nathan Walk, Austin P. Lund, and Timothy C. Ralph. Nondeterministic noiseless amplification via non-symplectic phase space transformations. New Journal of Physics, 15: 73014, 2013. 10.1088/​1367-2630/​15/​7/​073014.

[34] G. Y. Xiang, Timothy C. Ralph, Austin P. Lund, Nathan Walk, and Geoff J. Pryde. Heralded noiseless linear amplification and distillation of entanglement. Nature Photonics, 4: 316, 2010. 10.1038/​nphoton.2010.35.

[35] Anton Zeilinger, Michael A. Horne, and D. M. Greenberger. Publ. no. 3135. In NASA Conference, National Aeronautics and Space Administration, Code NTT, 1997.

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2020-09-22 11:12:27). On SAO/NASA ADS no data on citing works was found (last attempt 2020-09-22 11:12:27).