Error mitigation on a near-term quantum photonic device

Source Node: 844782

Daiqin Su1, Robert Israel1, Kunal Sharma2, Haoyu Qi1, Ish Dhand1, and Kamil Brádler1

1Xanadu, Toronto, Ontario, M5G 2C8, Canada
2Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA USA

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

Abstract

Photon loss is destructive to the performance of quantum photonic devices and therefore suppressing the effects of photon loss is paramount to photonic quantum technologies. We present two schemes to mitigate the effects of photon loss for a Gaussian Boson Sampling device, in particular, to improve the estimation of the sampling probabilities. Instead of using error correction codes which are expensive in terms of their hardware resource overhead, our schemes require only a small amount of hardware modifications or even no modification. Our loss-suppression techniques rely either on collecting additional measurement data or on classical post-processing once the measurement data is obtained. We show that with a moderate cost of classical post processing, the effects of photon loss can be significantly suppressed for a certain amount of loss. The proposed schemes are thus a key enabler for applications of near-term photonic quantum devices.

The Gaussian boson sampling (GBS) device is one of the most promising quantum photonic devices. It has recently been used to demonstrate the quantum computational advantage over classical computers in a specific sampling problem. The GBS device may also find practical applications, e.g., in solving molecular docking problems, in the near future. However, the performance of the GBS device is dramatically degraded by photon loss. In principle, the photon loss can be corrected using quantum error-correcting codes, but these codes introduce a large resource overhead. This work proposes two schemes to mitigate the effect of photon loss for the near-term GBS device, with a small hardware modification or even no modification. The price to pay is to perform multiple experiments and classical post-processing. This work finds that the effect of photon loss can be significantly suppressed with a moderate amount of classical resources. Therefore, the proposed loss mitigation schemes are essential for near-term applications of quantum photonic technologies.

► BibTeX data

► References

[1] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.032324

[2] J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[3] S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, Characterizing quantum supremacy in near-term devices, Nature Physics 14, 595 (2018).
https:/​/​doi.org/​10.1038/​s41567-018-0124-x

[4] S. Aaronson, and L. Chen, Complexity-theoretic foundations of quantum supremacy experiments, arXiv:1612.05903.
arXiv:1612.05903v1

[5] F. Arute, et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[6] M. J. Bremner, R. Jozsa, and D. 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).
https:/​/​doi.org/​10.1098/​rspa.2010.0301

[7] M. J. Bremner, A. Montanaro, and D. J. Shepherd, Average-case complexity versus approximate simulation of commuting quantum computations, Phys. Rev. Lett. 117, 080501 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.080501

[8] M. J. Bremner, A. Montanaro, and D. J. Shepherd, Achieving quantum supremacy with sparse and noisy commuting quantum computations, Quantum 1, 8 (2017).
https:/​/​doi.org/​10.22331/​q-2017-04-25-8

[9] S. Aaronson, A. Arkhipov, The computational complexity of linear optics, Proceedings of the forty-third annual ACM symposium on Theory of computing, 333-342 (2011).
https:/​/​doi.org/​10.1145/​1993636.1993682

[10] C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, Christine, and I. Jex, Gaussian Boson Sampling, Phys. Rev. Lett. 119, 170501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.170501

[11] S. Rahimi-Keshari, A. P. Lund, and T. C. Ralph, What Can Quantum Optics Say about Computational Complexity Theory?, Phys. Rev. Lett. 114, 060501 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.060501

[12] S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, Sufficient Conditions for Efficient Classical Simulation of Quantum Optics, Phys. Rev. X 6, 021039 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.021039

[13] A. Peruzzo, J. McClean, P. Shadbolt, M. Yung, X. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, A variational eigenvalue solver on a photonic quantum processor, Nature Communications 5, 4213 (2014).
https:/​/​doi.org/​10.1038/​ncomms5213

[14] E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028.
arXiv:1411.4028

[15] E. Farhi, and A. W. Harrow, Quantum supremacy through the quantum approximate optimization algorithm, arXiv:1602.07674.
arXiv:1602.07674

[16] K. Temme, S. Bravyi, and J. M. Gambetta, Error Mitigation for Short-Depth Quantum Circuits, Phys. Rev. Lett. 119, 180509 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.180509

[17] Y. Li, and S. C. Benjamin, Efficient Variational Quantum Simulator Incorporating Active Error Minimization, Phys. Rev. X 7, 021050 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.021050

[18] A. Kandala, K. Temme, A. D. Córcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Error mitigation extends the computational reach of a noisy quantum processor, Nature 567, 491 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1040-7

[19] S. Endo, S. C. Benjamin, and Y. Li, Practical Quantum Error Mitigation for Near-Future Applications, Phys. Rev. X 8, 031027 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.031027

[20] C. Song, J. Cui, H. Wang, J. Hao, H. Feng, H. and Li, Ying, Quantum computation with universal error mitigation on a superconducting quantum processor, Science Advances 5, (2019).
https:/​/​doi.org/​10.1126/​sciadv.aaw5686

[21] S. Zhang, Y. Lu, K. Zhang, W. Chen, Y. Li, J. Zhang, and K. Kim, Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system, Nature Communications 11, 1 (2020).
https:/​/​doi.org/​10.1038/​s41467-020-14376-z

[22] X. Bonet-Monroig, R. Sagastizabal, M. Singh, and T. E. O’Brien, Low-cost error mitigation by symmetry verification, Phys. Rev. A 98, 062339 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062339

[23] R. Sagastizabal, X. Bonet-Monroig, M. Singh, M. A. Rol, C. C. Bultink, X. Fu, C. H. Price, V. P. Ostroukh, N. Muthusubramanian, A. Bruno, M. Beekman, N. Haider, T. E. O’Brien, and L. DiCarlo, Experimental error mitigation via symmetry verification in a variational quantum eigensolver, Phys. Rev. A 100, 010302(R) (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.010302

[24] S. McArdle, X. Yuan, and S. Benjamin, Error-Mitigated Digital Quantum Simulation, Phys. Rev. Lett. 122, 180501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.180501

[25] X. Bonet-Monroig, R. Sagastizabal, M. Singh, and T. E. O’Brien, Low-cost error mitigation by symmetry verification, Phys. Rev. A 98, 062339 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062339

[26] M. Cerezo, K. Sharma, A. Arrasmith, and P. J. Coles, Variational quantum state eigensolver, arXiv:2004.01372.
arXiv:2004.01372

[27] J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New Journal of Physics 18, 023023 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​2/​023023

[28] K. Sharma, S. Khatri, M. Cerezo, and P. J. Coles, Noise resilience of variational quantum compiling, New Journal of Physics 22, 043006 (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​ab784c

[29] L. Cincio, K. Rudinger, M. Sarovar, and P. J. Coles, Machine learning of noise-resilient quantum circuits, PRX Quantum 2, 010324 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010324

[30] Y. Chen, M. Farahzad, S. Yoo, and T. Wei, Detector tomography on IBM quantum computers and mitigation of an imperfect measurement, Phys. Rev. A 100, 052315 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.052315

[31] M. R. Geller, and M. Sun, Efficient correction of multiqubit measurement errors, arXiv:2001.09980.
arXiv:2001.09980

[32] L. Funcke, T. Hartung, K. Jansen, S. Kühn, P. Stornati, and X. Wang, Measurement error mitigation in quantum computers through classical bit-flip correction, arXiv:2007.03663.
arXiv:2007.03663

[33] H. Kwon, and J. Bae, A hybrid quantum-classical approach to mitigating measurement errors in quantum algorithms, IEEE Transactions on Computers (2020).
https:/​/​doi.org/​10.1109/​TC.2020.3009664

[34] J. R. McClean, M. E. Kimchi-Schwartz, J. Carter, and W. A. de Jong, Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states, Phys. Rev. A 95, 042308 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.042308

[35] J. Sun, X. Yuan, T. Tsunoda, V. Vedral, S. C. Bejamin, and S. Endo, Mitigating Realistic Noise in Practical Noisy Intermediate-Scale Quantum Devices, Phys. Rev. Applied 15, 034026 (2021).
https:/​/​doi.org/​10.1103/​PhysRevApplied.15.034026

[36] A. Strikis, D. Qin, Y. Chen, B. C. Benjamin, and Y. Li, Learning-based quantum error mitigation, arXiv:2005.07601.
arXiv:2005.07601

[37] P. Czarnik, A. Arrasmith, P. J. Coles, and L. Cincio, Error mitigation with Clifford quantum-circuit data, arXiv:2005.10189.
arXiv:2005.10189

[38] A. Zlokapa, and A. Gheorghiu, A deep learning model for noise prediction on near-term quantum devices, arXiv:2005.10811.
arXiv:2005.10811

[39] J. Arrazola, and T. R. Bromley, Using Gaussian Boson Sampling to Find Dense Subgraphs, Phys. Rev. Lett. 121, 030503 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.030503

[40] K. Brádler, S. Friedland, J. Izaac, N. Killoran, and D. Su, Graph isomorphism and Gaussian boson sampling, Spec. Matrices 9, 166 (2021).
https:/​/​doi.org/​10.1515/​spma-2020-0132

[41] M. Schuld, K. Brádler, R. Israel, D. Su, and B. Gupt, Measuring the similarity of graphs with a Gaussian boson sampler, Phys. Rev. A 101, 032314 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.101.032314

[42] K. Brádler, R. Israel, M. Schuld, and D. Su, A duality at the heart of Gaussian boson sampling, arXiv:1910.04022.
arXiv:1910.04022v1

[43] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
https:/​/​doi.org/​10.1103/​RevModPhys.84.621

[44] K. Brádler, P. Dallaire-Demers, P. Rebentrost, D. Su, and C. Weedbrook, Gaussian boson sampling for perfect matchings of arbitrary graphs, Phys. Rev. A 98, 032310 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.032310

[45] H. Qi, D. J. Brod, N. Quesada, and R. García-Patrón, Regimes of Classical Simulability for Noisy Gaussian Boson Sampling, Phys. Rev. Lett. 124, 100502 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.100502

[46] W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walsmley, Optimal design for universal multiport interferometers, Optica 3, 1460 (2016).
https:/​/​doi.org/​10.1364/​OPTICA.3.001460

[47] M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Experimental Realization of Any Discrete Unitary Operator, Phys. Rev. Lett. 73, 58 (1994).
https:/​/​doi.org/​10.1103/​PhysRevLett.73.58

[48] M. Jacques, A. Samani, E. El-Fiky, D. Patel, X. Zhenping, and D. V. Plant, Optimization of thermo-optic phase-shifter design and mitigation of thermal crosstalk on the SOI platform, Opt. Express 27, 10456 (2019).
https:/​/​doi.org/​10.1364/​OE.27.010456

[49] A. Serafini, Quantum Continuous Variables: A Primer of Theoretical Methods (CRC Press, 2017).

[50] J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, Boson sampling for molecular vibronic spectra, Nature Photonics 9, 615 (2015).
https:/​/​doi.org/​10.1038/​nphoton.2015.153

[51] S. Rahimi-Keshari, M. A. Broome, R. Fickler, A. Fedrizzi, T. C. Ralph, and A. G. White, Direct characterization of linear-optical networks, Opt. Express 21, 13450 (2013).
https:/​/​doi.org/​10.1364/​OE.21.013450

[52] V. Giovannetti, A. S. Holevo, and R. García-Patrón, A Solution of Gaussian Optimizer Conjecture for Quantum Channels, Commun. Math. Phys. 334, 1553 (2015).
https:/​/​doi.org/​10.1007/​s00220-014-2150-6

[53] R. García-Patrón, J. Renema, and V. Shchesnovich, Simulating boson sampling in lossy architectures, Quantum 3, 169 (2019).
https:/​/​doi.org/​10.22331/​q-2019-08-05-169

[54] R. Kruse, C. S. Hamilton, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Detailed study of Gaussian boson sampling, Phys. Rev. A 100, 032326 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.032326

Cited by

[1] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, “Variational Quantum Algorithms”, arXiv:2012.09265.

[2] Tyler Volkoff, Zoë Holmes, and Andrew Sornborger, “Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning”, arXiv:2105.01049.

[3] Shreya P. Kumar, Leonhard Neuhaus, Lukas G. Helt, Haoyu Qi, Blair Morrison, Dylan H. Mahler, and Ish Dhand, “Mitigating linear optics imperfections via port allocation and compilation”, arXiv:2103.03183.

[4] Saad Yalouz, Bruno Senjean, Filippo Miatto, and Vedran Dunjko, “Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model”, arXiv:2103.15021.

The above citations are from SAO/NASA ADS (last updated successfully 2021-05-07 23:43:35). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-05-07 23:43:33).

Source: https://quantum-journal.org/papers/q-2021-05-04-452/

Time Stamp:

More from Quantum Journal