Robust Measurement Of Wave Function Topology On NISQ Quantum Computers

Abstract

Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are immune to local noise. Here, we present a strategy to measure topological invariants on quantum computers. We show that our strategy can be easily integrated with the variational quantum eigensolver (VQE) so that the topological properties of generic quantum many-body states can be characterized on current quantum hardware. We demonstrate the robust nature of the method by measuring topological invariants for both non-interacting and interacting models, and map out interacting quantum phase diagrams on quantum simulators and IBM quantum hardware.

Featured image: A generic strategy allows accurate calculations of Chern numbers on IBM’s quantum computers.

Popular summary

Calculations on current noisy intermediate-scale quantum (NISQ) hardware are susceptible to operation errors during the implementations of quantum circuits. Therefore, it is challenging to identify useful applications on which the present quantum hardware can be used. Here we provide a systematical strategy, which can be easily integrated with variational quantum algorithms, to characterize a key property of quantum matter: the wave function. Strikingly, we demonstrated that one important quantity that characterizes the wave function topology, the Chern number, can be calculated accurately on present quantum hardware without any error mitigation or error correction. Our work is an appealing demonstration that NISQ hardware might be a good platform to study quantum topological states and topological phenomena.

► BibTeX data

@article{Xiao2023robustmeasurementof, doi = {10.22331/q-2023-04-27-987}, url = {https://doi.org/10.22331/q-2023-04-27-987}, title = {Robust measurement of wave function topology on {NISQ} quantum computers}, author = {Xiao, Xiao and Freericks, J. K. and Kemper, A. F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {987}, month = apr, year = {2023}<br /> }

► References

[1] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
https://doi.org/10.1103/PhysRevLett.49.405

[2] Q. Niu, D. J. Thouless, and Y.-S. Wu, Phys. Rev. B 31, 3372 (1985).
https://doi.org/10.1103/PhysRevB.31.3372

[3] D. N. Sheng, L. Sheng, and Z. Y. Weng, Phys. Rev. B 73, 233406 (2006).
https://doi.org/10.1103/PhysRevB.73.233406

[4] H. Obuse, A. Furusaki, S. Ryu, and C. Mudry, Phys. Rev. B 76, 075301 (2007).
https://doi.org/10.1103/PhysRevB.76.075301

[5] J. Li, R.-L. Chu, J. K. Jain, and S.-Q. Shen, Phys. Rev. Lett. 102, 136806 (2009).
https://doi.org/10.1103/PhysRevLett.102.136806

[6] E. Prodan, J. Phys. A: Math. Theor. 44, 113001 (2011).
https://doi.org/10.1088/1751-8113/44/11/113001

[7] J. T. Chalker, M. Ortuno, and A. M. Somoza, Phys. Rev. B 83, 115317 (2011).
https://doi.org/10.1103/PhysRevB.83.115317

[8] J. Liu, A. C. Potter, K. T. Law, and P. A. Lee, Phys. Rev. Lett. 109, 267002 (2012).
https://doi.org/10.1103/PhysRevLett.109.267002

[9] A. M. Lobos, R. M. Lutchyn, and S. Das Sarma, Phys. Rev. Lett. 109, 146403 (2012).
https://doi.org/10.1103/PhysRevLett.109.146403

[10] E. J. Konig, P. M. Ostrovsky, I. V. Protopopov, I. V. Gornyi, I. S. Burmistrov, and A. D. Mirlin Phys. Rev. B 88, 035106 (2013).
https://doi.org/10.1103/PhysRevB.88.035106

[11] A. Altland, D. Bagrets, L. Fritz, A. Kamenev, and H. Schmiedt, Phys. Rev. Lett. 112, 206602 (2014).
https://doi.org/10.1103/PhysRevLett.112.206602

[12] I. Mondragon-Shem, T. L. Hughes, J. Song, and E. Prodan, Phys. Rev. Lett. 113, 046802 (2014).
https://doi.org/10.1103/PhysRevLett.113.046802

[13] J. Song, and E. Prodan, Phys. Rev. B 89, 224203 (2014).
https://doi.org/10.1103/PhysRevB.89.224203

[14] M. S. Foster, H.-Y. Xie, and Y.-Z. Chou, Phys. Rev. B 89, 155140 (2014).
https://doi.org/10.1103/PhysRevB.89.155140

[15] J. Wang, B. Lian, and S.-C. Zhang, Phys. Rev. B 89, 085106 (2014).
https://doi.org/10.1103/PhysRevB.89.085106

[16] C. Liu, W. Gao, B. Yang, and S. Zhang, Phys. Rev. Lett. 119, 183901 (2017).
https://doi.org/10.1103/PhysRevLett.119.183901

[17] E. J. Meier, F. A. An, A. Dauphin, M. Maffei, P. Massignan, T. L. Hughes, B. Gadway, Science 362, 929 (2018).
https://doi.org/10.1126/science.aat3406

[18] S. Stutzer, Y. Plotnik, Y. Lumer, P. Titum, N. Linder, M. Segev, M. C. Rechtsman, and A. Szameit, Nature 560, 461 (2018).
https://doi.org/10.1038/s41586-018-0418-2

[19] X. Xiao, arXiv:1802.02687 (2018).
https://doi.org/10.48550/arXiv.1802.02687
arXiv:1802.02687

[20] O. Shtanko, and R. Movassagh, Phys. Rev. Lett. 121, 126803 (2018).
https://doi.org/10.1103/PhysRevLett.121.126803

[21] T. Okugawa, P. Tang, A. Rubio, and D. M. Kennes, Phys. Rev. B 102, 201405(R) (2020).
https://doi.org/10.1103/PhysRevB.102.201405

[22] P. Roushan, C. Neill, Yu Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland and J. M. Martinis Nature 515, 241 (2014).
https://doi.org/10.1038/nature13891

[23] K. Choo, C. W. von Keyserlingk, N. Regnault, and T. Neupert, Phys. Rev. Lett. 121, 086808 (2018).
https://doi.org/10.1103/PhysRevLett.121.086808

[24] A. Smith, B. Jobst, A. G. Green, and F. Pollmann, Phys. Rev. Research 4, L022020 (2022).
https://doi.org/10.1103/PhysRevResearch.4.L022020

[25] D. Azses, R. Haenel, Y. Naveh, R. Raussendorf, E. Sela, and E. G. DallaTorre, Phys. Rev. Lett. 125, 120502 (2020).
https://doi.org/10.1103/PhysRevLett.125.120502

[26] F. Mei, Q. Guo, Y.-F. Yu, L. Xiao, S.-L. Zhu, and S. Jia, Phys. Rev. Lett. 125, 160503 (2020).
https://doi.org/10.1103/PhysRevLett.125.160503

[27] X. Xiao, J. K. Freericks, and A. F. Kemper, Quantum 5, 553 (2021).
https://doi.org/10.22331/q-2021-09-28-553

[28] E. Flurin, V. V. Ramasesh, S. Hacohen-Gourgy, L. S. Martin, N. Y. Yao, and I. Siddiqi, Phys. Rev. X 7, 031023 (2017).
https://doi.org/10.1103/PhysRevX.7.031023

[29] X. Zhan, L. Xiao, Z. Bian, K. Wang, X. Qiu, B. C. Sanders, W. Yi, and P. Xue, Phys. Rev. Lett. 119, 130501 (2017).
https://doi.org/10.1103/PhysRevLett.119.130501

[30] X.-Y. Xu, Q.-Q. Wang, W.-W. Pan, K. Sun, J.-S. Xu, G. Chen, J.-S. Tang, M. Gong, Y.-J. Han, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 120, 260501 (2018).
https://doi.org/10.1103/PhysRevLett.120.260501

[31] A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, and B. Vermersch, Sci. Adv. 6, eaaz3666 (2020).
https://doi.org/10.1126/sciadv.aaz3666

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

[33] A. Kandala, K. Temme, A. D. Corcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Nature 567, 491 (2019).
https://doi.org/10.1038/s41586-019-1040-7

[34] K. E. Hamilton, and R. C. Pooser, Quantum Machine Intelligence 2, 10 (2020).
https://doi.org/10.1007/s42484-020-00021-x

[35] A. Cervera-Lierta, Quantum 2, 114 (2018).
https://doi.org/10.22331/q-2018-12-21-114

[36] K. Yeter-Aydeniz, R. C. Pooser, and G. Siopsis, npj Quantum Inf. 6, 63 (2020).
https://doi.org/10.1038/s41534-020-00290-1

[37] G. E. Volovik, JETP Lett. 70, 609 (1999).
https://doi.org/10.1134/1.568223

[38] N. Read, and D. Green, Phys. Rev. B 61, 10267 (2000).
https://doi.org/10.1103/PhysRevB.61.10267

[39] T. Fukui, Y. Hutsugai, and H. Suzuki, J. Phys. Soc. Jpn. 74, 1674 (2005).
https://doi.org/10.1143/JPSJ.74.1674

[40] P. J. J. O’malley, et al. Phys. Rev. X 6, 031007 (2016).
https://doi.org/10.1103/PhysRevX.6.031007

[41] A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Nature 549, 242 (2017).
https://doi.org/10.1038/nature23879

[42] C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, Nature 569, 355 (2019).
https://doi.org/10.1038/s41586-019-1177-4

[43] X. Yaun, S. Endo, Q. Zhao, Y. Li and S. C. Benjamin, Quantum 3, 191 (2019).
https://doi.org/10.22331/q-2019-10-07-191

[44] H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall Nat. Commun. 10, 3007 (2019).
https://doi.org/10.1038/s41467-019-10988-2

[45] Y. Hatsugai, and M. Kohmoto, J. Phys. Soc. Jpn 61, 2056 (1992).
https://doi.org/10.1143/JPSJ.61.2056

[46] K. Kudo, H. Watanabe, T. Kariyado, and Y. Hatsugai, Phys. Rev. Lett. 122, 146601 (2019).
https://doi.org/10.1103/PhysRevLett.122.146601

[47] P. W. Philips, L. Yeo, and E. W. Huang Nat. Phys. 16, 1175 (2020).
https://doi.org/10.1038/s41567-020-0988-4

[48] X.-L. Qi, Y. S. Wu and S. C. Zhang, Phys. Rev. B 74, 085308 (2006).
https://doi.org/10.1103/PhysRevB.74.085308

[49] H.-Q. Wu, Y.-Y. He, C. Fang, Z. Y. Meng and Z.-Y. Lu, Phys. Rev. Lett. 117, 066403 (2016).
https://doi.org/10.1103/PhysRevLett.117.066403

[50] C.-E. Bardyn, L. Wawer, A. Altland, M. Fleischhauer, and S. Diehl, Phys. Rev. X 8, 011035 (2018).
https://doi.org/10.1103/PhysRevX.8.011035

[51] D. Aharonov, V. Jones, and Z. Landau, Algorithmica 55, 395 (2009).
https://doi.org/10.1007/s00453-008-9168-0

[52] B. Murta, G. Catarina, J. Fernandez-Rossier Phys. Rev. A 101, 020302 (2020).
https://doi.org/10.1103/PhysRevA.101.020302

[53] G. Aleksandrowicz, et al. Qiskit: An open-source framework for quantum computing. (2019).
https://doi.org/10.5281/ZENODO.2562111

[54] E. Knill, Nature 434, 39 (2005).
https://doi.org/10.1038/nature03350

[55] A. Cross, D. P. Divincenzo, and B. M. Terhal, Quantum Info. Comput. 9, 541 (2009).
https://doi.org/10.48550/arXiv.0711.1556

[56] J. Lee, W. J. Huggins, M. Head-Gordon and K. B. Whaley, J. Chem. Theory Comput. 15, 311 (2019).
https://doi.org/10.1021/acs.jctc.8b01004

[57] J. Chen, H.-P. Cheng and J. K. Freericks, J. Chem. Theory Comput. 17, 841 (2021).
https://doi.org/10.1021/acs.jctc.0c01052

[58] Y. Yao, F. Zhang, C.-Z. Wang, K.-M. Ho, and P. P. Orth Phys. Rev. Research 3, 013184 (2021).
https://doi.org/10.1103/PhysRevResearch.3.013184

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

[60] Z.-P. Cian, H. Dehghani, A. Elben, B. Vermersch, G. Zhu, M. Barkeshli, P. Zoller, and M. Hafezi, Phys. Rev. Lett. 126, 050501 (2021).
https://doi.org/10.1103/PhysRevLett.126.050501

[61] I. G. Ryabinkin, T.-C. Yen, S. N. Genin, and A. F. Izmaylov, J. Chem. Theory Comput. 14, 6317 (2018).
https://doi.org/10.1021/acs.jctc.8b00932

[62] M. Motta, C. Sun, A. T. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. Brandao, G. K.-L. Chan, Nat. Phys. 16, 205 (2020).
https://doi.org/10.1038/s41567-019-0704-4

[63] D. A. Fedorov, B. Peng, N. Govind, and Y. Alexeev, arXiv: 2103.08505 (2021).
https://doi.org/10.48550/arXiv.2103.08505

Cited by

[1] Efekan Kökcü, Daan Camps, Lindsay Bassman, J. K. Freericks, Wibe A. de Jong, Roel Van Beeumen, and Alexander F. Kemper, “Algebraic compression of quantum circuits for Hamiltonian evolution”, Physical Review A 105 3, 032420 (2022).

[2] Huai-Chun Chang and Hsiu-Chuan Hsu, “Digital quantum simulation of dynamical topological invariants on near-term quantum computers”, Quantum Information Processing 21 1, 41 (2022).

[3] Emiel Koridon, Joana Fraxanet, Alexandre Dauphin, Lucas Visscher, Thomas E. O’Brien, and Stefano Polla, “A hybrid quantum algorithm to detect conical intersections”, arXiv:2304.06070, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-04-28 12:01:43). 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 2023-04-28 12:01:42).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

Plato Data Intelligence.
Vertical Search & Ai.

Robust measurement of wave function topology on NISQ quantum computers

Abstract

Popular summary

► BibTeX data

► References

Cited by

Taiwan’s ACE Exchange Founder and Associates Face 20-Year Prison Sentences in Fraud and Money Laundering Case

DOJ insists Tornado Cash operated as a ‘commercial enterprise’

Latest Intelligence

Top 8 ICOs for 2024: BlockDAG Leads with Record-Breaking Presale

Upbit Dominates South Korea’s Crypto Market, Ranking Top 5 Globally: Report

Justin Biever’s NFT Portfolio Lost Over 94% of Its Value, Gong from $2 Million to $100,000

Young Investor Skyrockets Initial $500 To $20,000 In Under One Week With Emerging Competitor To Shiba Inu (SHIB) – CryptoInfoNet

CFI, Deriv, Gold-i and More: Executive Moves of the Week

Institutional Interest in Crypto Assets Surges in Canada: KPMG Report

Chat with us

Plato Data Intelligence.Vertical Search & Ai.

Robust measurement of wave function topology on NISQ quantum computers

Abstract

Cited by

Latest Intelligence

Chat with us

Plato Data Intelligence.
Vertical Search & Ai.