Nondestructive classification of quantum states using an algorithmic quantum computer

Abstract

Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an input to the device that may find numerous applications in quantum information technologies. In the present paper, we address a scheme of a classification of input states, which is nondestructive and deterministic for certain inputs, while probabilistic, in general case. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically. We perform proof-of-principle implementation of this idea using superconducting quantum processor of IBM Quantum Experience. Another aspect we are interested in is a mitigation of errors occurring due to the quantum device imperfections. We apply a series of heuristic tricks at the stage of classical postprocessing in order to improve raw experimental data and to recognize patterns in them. These ideas may find applications in other realization of hybrid quantum-classical computations with noisy quantum machines.

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References

  1. Aaronson S (2015) Read the fine print. Nat Phys 11:291

    Article  Google Scholar 

  2. Adcock J, Allen E, Day M, Frick S, Hinchliff J, Johnson M, Morley-Short S, Pallister S, Price A, Stanisic S (2015) Advances in quantum machine learning. arXiv:1512.02900

  3. Amin MH, Andriyash E, Rolfe J, Kulchytskyy B, Melko R (2018) Quantum boltzmann machine. Phys Rev X 8:021050

    Google Scholar 

  4. Arunachalam S, Gheorghiu V, Jochym-O’Connor T, Mosca M, Srinivasan PV (2015) On the robustness of bucket brigade quantum RAM. New J Phys 17:123010

    Article  Google Scholar 

  5. Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2017) Quantum machine learning. Nature 549:19

    Article  Google Scholar 

  6. Cai X-D, Wu D, Su Z-E, Chen M-C, Wang X-L, Li L, Liu N-L, Lu C-Y, Pan J-W (2015) Entanglement-based machine learning on a quantum computer. Phys Rev Lett 114:110504

    Article  Google Scholar 

  7. Degen CL, Reinhard F, Cappellaro P (2017) Quantum sensing. Rev Mod Phys 89:035002

    MathSciNet  Article  Google Scholar 

  8. Endo S, Benjamin SC, Li Y (2018) Practical quantum error mitigation for near-future applications. Phys Rev X 8:031027

    Google Scholar 

  9. Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. arXiv:1411.4028

  10. Granade CE, Ferrie C, Wiebe N, Cory DG (2012) Robust online hamiltonian learning. New J Phys 14:103013

    MathSciNet  Article  Google Scholar 

  11. Kandala A, Mezzacapo A, Temme K, Takita M, Brink M, Chow JM, Gambetta JM (2017) Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549:242

    Article  Google Scholar 

  12. Li Y, Benjamin SC (2017) Efficient variational quantum simulator incorporating active error minimization. Phys Rev X 7:021050

    Google Scholar 

  13. Li Z, Liu X, Xu N, Du J (2015) Experimental realization of a quantum support vector machine. Phys Rev Lett 114:140504

    Article  Google Scholar 

  14. Lloyd S (2008) Enhanced sensitivity of photodetection via quantum illumination. Science 321:1463

    Article  Google Scholar 

  15. McClean JR, Romero J, Babbush R, Aspuru-Guzik A (2016) The theory of variational hybrid quantum-classical algorithms. New J Phys 18:023023

    Article  Google Scholar 

  16. McClean JR, Kimchi-Schwartz ME, Carter J, de Jong WA (2017) Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys Rev A 95:042308

    Article  Google Scholar 

  17. Peruzzo A, McClean J, Shadbolt P, Yung M-H, Zhou X-Q, Love PJ, Aspuru-Guzik A, O’Brien JL (2014) A variational eigenvalue solver on a photonic quantum processor. Nat Comm 5:4213

    Article  Google Scholar 

  18. Preskill J (2018) Quantum computing in the NISQ era and beyond. Quantum 2:79

    Article  Google Scholar 

  19. Ristè D, da Silva MP, Ryan CA, Cross AW, Smolin JA, Gambetta JM, Chow JM, Johnson BR (2017) Demonstration of quantum advantage in machine learning. npj Quantum Information 3:16

    Article  Google Scholar 

  20. Schuld M, Sinaiskiy I, Petruccione F (2015a) An introduction to quantum machine learning. Contemp Phys 56(2):1034

    Article  Google Scholar 

  21. Schuld M, Sinayskiy I, Petruccione F (2015b) Simulating a perceptron on a quantum computer. Phys Lett A 379:660

    Article  Google Scholar 

  22. Tan S-H, Erkmen BI, Giovannetti V, Guha S, Lloyd S, Maccone L, Pirandola S, Shapiro JH (2008) Quantum illumination with gaussian states. Phys Rev Lett 101:253601

    Article  Google Scholar 

  23. Temme K, Bravyi S, Gambetta JM (2017) Error mitigation for short-depth quantum circuits. Phys Rev Lett 119:180509

    MathSciNet  Article  Google Scholar 

  24. Wiebe N, Braun D, Lloyd S (2012) Quantum algorithm for data fitting. Phys Rev Lett 109:050505

    Article  Google Scholar 

  25. Wiebe N, Granade C, Ferrie C, Cory DG (2014) Hamiltonian learning and certification using quantum resources. Phys Rev Lett 112:190501

    Article  Google Scholar 

  26. Zhukov AA, Remizov SV, Pogosov WV, Lozovik YE. (2018) Algorithmic simulation of far-from-equilibrium dynamics using quantum computer. Quantum Inf Process 17:223

    MathSciNet  Article  Google Scholar 

  27. Zhukov AA, Kiktenko EO, Elistratov AA, Pogosov WV, Lozovik YE (2019) Quantum communication protocols as a benchmark for programmable quantum computers. Quantum Inf Process 18:31

    Article  Google Scholar 

Download references

Acknowledgments

We acknowledge use of the IBM Quantum Experience for this work. The viewpoints expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum Experience team. W. V. P. acknowledges a support from RFBR (project no. 19-02-00421).

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Correspondence to W. V. Pogosov.

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Babukhin, D.V., Zhukov, A.A. & Pogosov, W.V. Nondestructive classification of quantum states using an algorithmic quantum computer. Quantum Mach. Intell. 1, 87–96 (2019). https://doi.org/10.1007/s42484-019-00010-9

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Keywords

  • Quantum computing
  • Quantum data processing
  • Postprocessing
  • Quantum error correction
  • Error mitigation