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Analysis of circuit imperfections in BosonSampling

Leverrier, Anthony, Garcia-Patron, Raul·2015·Quantum Information and Computation
DOI 10.26421/qic15.5-6-8
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Abstract

BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this work, we investigate whether an experimentally realistic BosonSampler can really solve BosonSampling without any fault-tolerance mechanism. More precisely, we study how the unavoidable errors linked to an imperfect calibration of the optical elements affect the final result of the computation. We show that the fidelity of each optical element must be at least 1 − O(1/n^2 ), where n refers to the number of single photons in the scheme. Such a requirement seems to be achievable with state-of-the-art equipment.

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  • In 2017, new classical algorithms were proposed to solve BosonSampling for systems with dimensionality larger than that allowed by near-term technological advances.

    “Nevertheless, in 2017 new classical algorithms have been proposed to solve Boson-Sampling for systems with dimensionality larger than that allowed by near-term technological advances [564,565,572,573,593,594]”

    From Photonic quantum information processing: a review (2019) · cites this paper as [594]

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Research works printed but not linked: 15

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  3. John Preskill. Quantum computing and the entanglement frontier. arXiv preprint arXiv:1203.5813, 2012. · arXiv
  4. Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. Theory of Computing, 9(4):143-252, 2013.
  5. Justin B Spring, Benjamin J Metcalf, Peter C Humphreys, W Steven Kolthammer, Xian-Min Jin, Marco Barbieri, Animesh Datta, Nicholas Thomas-Peter, Nathan K Langford, Dmytro Kundys, et al. Boson sampling on a photonic chip. Science, 339(6121):798-801, 2013.
  6. Larry J Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3(1):1-22, 1976.
  7. Alex Arkhipov and Greg Kuperberg. The bosonic birthday paradox. arXiv preprint arXiv:1106.0849, 2011. · arXiv
  8. Michael Reck, Anton Zeilinger, Herbert J Bernstein, and Philip Bertani. Experimental realization of any discrete unitary operator. Physical Review Letters, 73(1):58, 1994.
  9. Stefan Scheel. Permanents in linear optical networks. arXiv preprint quant-ph/0406127, 2004. · arXiv
  10. C. Gogolin, M. Kliesch, L. Aolita, and J. Eisert. Boson-sampling in the light of sample complexity. arXiv preprint arXiv:1306.3995, 2013. · arXiv
  11. Peter P Rohde and Timothy C Ralph. Error tolerance of the boson-sampling model for linear optics quantum computing. Physical Review A, 85(2):022332, 2012.
  12. Peter P Rohde. Optical quantum computing with photons of arbitrarily low fidelity and purity. Physical Review A, 86(5):052321, 2012.
  13. Sanjeev Arora, Arnab Bhattacharyya, Rajsekar Manokaran, and Sushant Sachdeva. Testing per- manent oracles-revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pages 362-373. Springer, 2012.
  14. Bai-Ni Guo and Feng Qi. Sharp bounds for harmonic numbers. Applied Mathematics and Com- putation, 218(3):991-995, 2011.
  15. Joel A Tropp. User-friendly tail bounds for sums of random matrices. Foundations of Computa- tional Mathematics, 12(4):389-434, 2012.

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Metadata

Authors
Leverrier, A., & Garcia-Patron, R.
Venue
Quantum Information and Computation
Publisher
Rinton Press
Published
2015-04
Pages
489-512
ISSN
1533-7146
DOI
10.26421/qic15.5-6-8
Cited by
17
References
4

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