Overhead for simulating a non-local channel with local channels by quasiprobability sampling

Kosuke Mitarai1,2,3 and Keisuke Fujii1,2,4

1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
2Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Japan.
3JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
4Center for Emergent Matter Science, RIKEN, Wako Saitama 351-0198, Japan

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Abstract

As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations by local ones. Such substitution can be performed by decomposing a non-local channel into a linear combination of local channels and simulating the original channel with a quasiprobability-based method. In this work, we first define a quantity that we call channel robustness of non-locality, which quantifies the cost for the decomposition. While this quantity is challenging to calculate for a general non-local channel, we give an upper bound for a general two-qubit unitary channel by providing an explicit decomposition. The decomposition is obtained by generalizing our previous work whose application has been restricted to a certain form of two-qubit unitary. This work develops a framework for a resource reduction suitable for first-generation quantum devices.

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[1] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. P. Harrigan, M. J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S. Humble, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. V. Klimov, S. Knysh, A. Korotkov, F. Kostritsa, D. Landhuis, M. Lindmark, E. Lucero, D. Lyakh, S. Mandrà, J. R. McClean, M. McEwen, A. Megrant, X. Mi, K. Michielsen, M. Mohseni, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Y. Niu, E. Ostby, A. Petukhov, J. C. Platt, C. Quintana, E. G. Rieffel, P. Roushan, N. C. Rubin, D. Sank, K. J. Satzinger, V. Smelyanskiy, K. J. Sung, M. D. Trevithick, A. Vainsencher, B. Villalonga, T. White, Z. J. Yao, P. Yeh, A. Zalcman, H. Neven, and J. M. Martinis, Nature 574, 505 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[2] J. Preskill, Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[3] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien, Nature Communications 5, 4213 (2014).
https:/​/​doi.org/​10.1038/​ncomms5213

[4] S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Rev. Mod. Phys. 92, 015003 (2020).
https:/​/​doi.org/​10.1103/​RevModPhys.92.015003

[5] E. Farhi, J. Goldstone, and S. Gutmann, ``A quantum approximate optimization algorithm,'' (2014), arXiv:1411.4028 [quant-ph].
arXiv:1411.4028

[6] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Phys. Rev. A 98, 032309 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.032309

[7] E. Farhi and H. Neven, ``Classification with quantum neural networks on near term processors,'' (2018), arXiv:1802.06002 [quant-ph].
arXiv:1802.06002

[8] C. Bravo-Prieto, R. LaRose, M. Cerezo, Y. Subasi, L. Cincio, and P. J. Coles, ``Variational quantum linear solver,'' (2019), arXiv:1909.05820 [quant-ph].
arXiv:1909.05820

[9] R. LaRose, A. Tikku, E. O'Neel-Judy, L. Cincio, and P. J. Coles, npj Quantum Information 5, 8 (2019).
https:/​/​doi.org/​10.1038/​s41534-019-0167-6

[10] T. Peng, A. W. Harrow, M. Ozols, and X. Wu, Phys. Rev. Lett. 125, 150504 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.150504

[11] K. Mitarai and K. Fujii, New Journal of Physics , accepted (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​abd7bc

[12] K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.180509

[13] S. Endo, S. C. Benjamin, and Y. Li, Phys. Rev. X 8, 031027 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.031027

[14] H. Pashayan, J. J. Wallman, and S. D. Bartlett, Phys. Rev. Lett. 115, 070501 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.070501

[15] M. Howard and E. Campbell, Phys. Rev. Lett. 118, 090501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.090501

[16] S. Bravyi, G. Smith, and J. A. Smolin, Phys. Rev. X 6, 021043 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.021043

[17] R. S. Bennink, E. M. Ferragut, T. S. Humble, J. A. Laska, J. J. Nutaro, M. G. Pleszkoch, and R. C. Pooser, Phys. Rev. A 95, 062337 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.062337

[18] J. R. Seddon and E. T. Campbell, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20190251 (2019).
https:/​/​doi.org/​10.1098/​rspa.2019.0251

[19] B. Kraus and J. I. Cirac, Phys. Rev. A 63, 062309 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.63.062309

[20] J. Zhang, J. Vala, S. Sastry, and K. B. Whaley, Phys. Rev. A 67, 042313 (2003).
https:/​/​doi.org/​10.1103/​PhysRevA.67.042313

[21] F.-Z. Kong, J.-L. Zhao, M. Yang, and Z.-L. Cao, Phys. Rev. A 92, 012127 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.92.012127

[22] Y. Ibe, Y. O. Nakagawa, T. Yamamoto, K. Mitarai, Q. Gao, and T. Kobayashi, ``Calculating transition amplitudes by variational quantum eigensolvers,'' (2020), arXiv:2002.11724 [quant-ph].
arXiv:2002.11724

[23] K. Mitarai and K. Fujii, Phys. Rev. Research 1, 013006 (2019).
https:/​/​doi.org/​10.1103/​PhysRevResearch.1.013006

[24] H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, Phys. Rev. Lett. 87, 167902 (2001).
https:/​/​doi.org/​10.1103/​PhysRevLett.87.167902

[25] J. C. Garcia-Escartin and P. Chamorro-Posada, Phys. Rev. A 87, 052330 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.052330

Cited by

[1] Xiao Yuan, Jinzhao Sun, Junyu Liu, Qi Zhao, and You Zhou, "Quantum Simulation with Hybrid Tensor Networks", Physical Review Letters 127 4, 040501 (2021).

[2] Keisuke Fujii, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers", arXiv:2007.10917.

[3] Yasunari Suzuki, Suguru Endo, Keisuke Fujii, and Yuuki Tokunaga, "Quantum error mitigation for fault-tolerant quantum computing", arXiv:2010.03887.

The above citations are from Crossref's cited-by service (last updated successfully 2021-08-02 08:40:36) and SAO/NASA ADS (last updated successfully 2021-08-02 08:40:38). The list may be incomplete as not all publishers provide suitable and complete citation data.