Robust measurement of wave function topology on NISQ quantum computers

Xiao, Xiao; Freericks, James K.; Kemper, A. F.

doi:10.22331/q-2023-04-27-987

Title: Robust measurement of wave function topology on NISQ quantum computers

Journal Article · 27 April 2023 · Quantum

DOI: https://doi.org/10.22331/q-2023-04-27-987 · OSTI ID:2234347

Xiao, Xiao ^[1]; Freericks, James K. ^[2]; Kemper, A. F. ^[1]

North Carolina State University, Raleigh, NC (United States)
Georgetown University, Washington, DC (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Georgetown Univ., Washington, DC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019469

OSTI ID:: 2234347

Journal Information:: Quantum, Vol. 7; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (63)

Photonic topological Anderson insulators Stützer, Simon; Plotnik, Yonatan; Lumer, Yaakov Nature, Vol. 560, Issue 7719 https://doi.org/10.1038/s41586-018-0418-2	journal	August 2018
Interaction and disorder effects in three-dimensional topological insulator thin films König, E. J.; Ostrovsky, P. M.; Protopopov, I. V. Physical Review B, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevB.88.035106	journal	July 2013
Interaction and disorder effects in 3D topological insulator thin films König, E. J.; Ostrovsky, P. M.; Protopopov, I. V. arXiv https://doi.org/10.48550/arxiv.1305.2820	text	January 2013
Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization Wu, Han-Qing; He, Yuan-Yao; Fang, Chen Physical Review Letters, Vol. 117, Issue 6 https://doi.org/10.1103/PhysRevLett.117.066403	journal	August 2016
Self-verifying variational quantum simulation of lattice models Kokail, C.; Maier, C.; van Bijnen, R. Nature, Vol. 569, Issue 7756 https://doi.org/10.1038/s41586-019-1177-4	journal	May 2019
Observation of topological transitions in interacting quantum circuits Roushan, P.; Neill, C.; Chen, Yu Nature, Vol. 515, Issue 7526 https://doi.org/10.1038/nature13891	journal	November 2014
Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks Zhan, Xiang; Xiao, Lei; Bian, Zhihao Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.130501	journal	September 2017
Topological phase transitions induced by disorder in magnetically doped (Bi,Sb)2Te3 thin films Okugawa, Takuya; Tang, Peizhe; Rubio, Angel Physical Review B, Vol. 102, Issue 20 https://doi.org/10.1103/PhysRevB.102.201405	journal	November 2020
Error-mitigated data-driven circuit learning on noisy quantum hardware Hamilton, Kathleen E.; Pooser, Raphael C. Quantum Machine Intelligence, Vol. 2, Issue 1 https://doi.org/10.1007/s42484-020-00021-x	journal	June 2020
Gutzwiller hybrid quantum-classical computing approach for correlated materials Yao, Yongxin; Zhang, Feng; Wang, Cai-Zhuang Physical Review Research, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevResearch.3.013184	journal	February 2021
Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder Mondragon-Shem, Ian; Hughes, Taylor L.; Song, Juntao Physical Review Letters, Vol. 113, Issue 4 https://doi.org/10.1103/PhysRevLett.113.046802	journal	July 2014
Identification of Symmetry-Protected Topological States on Noisy Quantum Computers Azses, Daniel; Haenel, Rafael; Naveh, Yehuda Physical Review Letters, Vol. 125, Issue 12 https://doi.org/10.1103/PhysRevLett.125.120502	journal	September 2020
Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware Xiao, Xiao; Freericks, J. K.; Kemper, A. F. Quantum, Vol. 5 https://doi.org/10.22331/q-2021-09-28-553	journal	September 2021
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation Lee, Joonho; Huggins, William J.; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 15, Issue 1 https://doi.org/10.1021/acs.jctc.8b01004	journal	November 2018
Zero-Bias Peaks in the Tunneling Conductance of Spin-Orbit-Coupled Superconducting Wires with and without Majorana End-States Liu, Jie; Potter, Andrew C.; Law, K. T. Physical Review Letters, Vol. 109, Issue 26 https://doi.org/10.1103/PhysRevLett.109.267002	journal	December 2012
Fermion zero modes on vortices in chiral superconductors Volovik, G. E. Journal of Experimental and Theoretical Physics Letters, Vol. 70, Issue 9 https://doi.org/10.1134/1.568223	journal	November 1999
Quantum Computing in the NISQ era and beyond Preskill, John Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-06-79	journal	August 2018
Stability of Periodically Driven Topological Phases against Disorder Shtanko, Oles; Movassagh, Ramis Physical Review Letters, Vol. 121, Issue 12 https://doi.org/10.1103/PhysRevLett.121.126803	journal	September 2018
Observation of the topological Anderson insulator in disordered atomic wires Meier, Eric J.; An, Fangzhao Alex; Dauphin, Alexandre Science, Vol. 362, Issue 6417 https://doi.org/10.1126/science.aat3406	journal	October 2018
Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors Qi, Xiao-Liang; Wu, Yong-Shi; Zhang, Shou-Cheng Physical Review B, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevB.74.085308	journal	August 2006
Probing the Topology of Density Matrices Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevX.8.011035	journal	February 2018
Theory of variational quantum simulation Yuan, Xiao; Endo, Suguru; Zhao, Qi Quantum, Vol. 3 https://doi.org/10.22331/q-2019-10-07-191	journal	October 2019
Exact theory for superconductivity in a doped Mott insulator Phillips, Philip W.; Yeo, Luke; Huang, Edwin W. Nature Physics, Vol. 16, Issue 12 https://doi.org/10.1038/s41567-020-0988-4	journal	July 2020
Two-dimensional spin-filtered chiral network model for theZ2quantum spin-Hall effect Obuse, Hideaki; Furusaki, Akira; Ryu, Shinsei Physical Review B, Vol. 76, Issue 7 https://doi.org/10.1103/PhysRevB.76.075301	journal	August 2007
Crossing a topological phase transition with a quantum computer Smith, Adam; Jobst, Bernhard; Green, Andrew G. Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.L022020	journal	April 2022
Universal scaling of the quantum anomalous Hall plateau transition Wang, Jing; Lian, Biao; Zhang, Shou-Cheng Physical Review B, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevB.89.085106	journal	February 2014
Interplay of Disorder and Interaction in Majorana Quantum Wires Lobos, Alejandro M.; Lutchyn, Roman M.; Das Sarma, S. Physical Review Letters, Vol. 109, Issue 14 https://doi.org/10.1103/PhysRevLett.109.146403	journal	October 2012
Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem Condensed Matter Physics, Vol. 9, Issue 3 https://doi.org/10.5488/cmp.9.3.603	journal	January 2006
Topological protection, disorder, and interactions: Survival at the surface of three-dimensional topological superconductors Foster, Matthew S.; Xie, Hong-Yi; Chou, Yang-Zhi Physical Review B, Vol. 89, Issue 15 https://doi.org/10.1103/PhysRevB.89.155140	journal	April 2014
Many-body topological invariants from randomized measurements in synthetic quantum matter Elben, Andreas; Yu, Jinlong; Zhu, Guanyu Science Advances, Vol. 6, Issue 15 https://doi.org/10.1126/sciadv.aaz3666	journal	April 2020
Quantized Hall Conductance in a Two-Dimensional Periodic Potential Thouless, D. J.; Kohmoto, M.; Nightingale, M. P. Physical Review Letters, Vol. 49, Issue 6 https://doi.org/10.1103/PhysRevLett.49.405	journal	August 1982
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial Aharonov, Dorit; Jones, Vaughan; Landau, Zeph Algorithmica, Vol. 55, Issue 3 https://doi.org/10.1007/s00453-008-9168-0	journal	March 2008
VQE Method: A Short Survey and Recent Developments Fedorov, Dmitry A.; Peng, Bo; Govind, Niranjan arXiv https://doi.org/10.48550/arXiv.2103.08505	preprint	January 2021
Many-Body Chern Number from Statistical Correlations of Randomized Measurements Cian, Ze-Pei; Dehghani, Hossein; Elben, Andreas Physical Review Letters, Vol. 126, Issue 5 https://doi.org/10.1103/PhysRevLett.126.050501	journal	February 2021
Quantized Hall conductance as a topological invariant Niu, Qian; Thouless, D. J.; Wu, Yong-Shi Physical Review B, Vol. 31, Issue 6 https://doi.org/10.1103/PhysRevB.31.3372	journal	March 1985
Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State Using the IBM Quantum Computer Choo, Kenny; von Keyserlingk, Curt W.; Regnault, Nicolas Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.086808	journal	August 2018
Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms Yeter-Aydeniz, Kübra; Pooser, Raphael C.; Siopsis, George npj Quantum Information, Vol. 6, Issue 1 https://doi.org/10.1038/s41534-020-00290-1	journal	July 2020
Many-Body Chern Number without Integration Kudo, Koji; Watanabe, Haruki; Kariyado, Toshikaze Physical Review Letters, Vol. 122, Issue 14 https://doi.org/10.1103/PhysRevLett.122.146601	journal	April 2019
Quantum computing with realistically noisy devices Knill, E. Nature, Vol. 434, Issue 7029 https://doi.org/10.1038/nature03350	journal	March 2005
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution Motta, Mario; Sun, Chong; Tan, Adrian T. K. Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0704-4	journal	November 2019
Spin quantum Hall effect and plateau transitions in multilayer network models Chalker, J. T.; Ortuño, M.; Somoza, A. M. Physical Review B, Vol. 83, Issue 11 https://doi.org/10.1103/PhysRevB.83.115317	journal	March 2011
Topological Anderson Insulator Li, Jian; Chu, Rui-Lin; Jain, J. K. Physical Review Letters, Vol. 102, Issue 13 https://doi.org/10.1103/PhysRevLett.102.136806	journal	April 2009
Measuring the Winding Number in a Large-Scale Chiral Quantum Walk Xu, Xiao-Ye; Wang, Qin-Qin; Pan, Wei-Wei Physical Review Letters, Vol. 120, Issue 26 https://doi.org/10.1103/PhysRevLett.120.260501	journal	June 2018
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances Fukui, Takahiro; Hatsugai, Yasuhiro; Suzuki, Hiroshi Journal of the Physical Society of Japan, Vol. 74, Issue 6 https://doi.org/10.1143/JPSJ.74.1674	journal	June 2005
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect Read, N.; Green, Dmitry Physical Review B, Vol. 61, Issue 15 https://doi.org/10.1103/PhysRevB.61.10267	journal	April 2000
Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer Ryabinkin, Ilya G.; Yen, Tzu-Ching; Genin, Scott N. Journal of Chemical Theory and Computation, Vol. 14, Issue 12 https://doi.org/10.1021/acs.jctc.8b00932	journal	November 2018
Quantum Hall effect in graphene: Disorder effect and phase diagram Sheng, D. N.; Sheng, L.; Weng, Z. Y. Physical Review B, Vol. 73, Issue 23 https://doi.org/10.1103/PhysRevB.73.233406	journal	June 2006
Stability of Kramers Majorana doublets: the effects of interactions and disorders Xiao, Xiao arXiv https://doi.org/10.48550/arXiv.1802.02687	preprint	January 2018
Exact Ising model simulation on a quantum computer Cervera-Lierta, Alba Quantum, Vol. 2 https://doi.org/10.22331/q-2018-12-21-114	journal	December 2018
Disordered topological insulators: a non-commutative geometry perspective Prodan, Emil Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 11 https://doi.org/10.1088/1751-8113/44/11/113001	journal	February 2011
A comparative code study for quantum fault-tolerance Cross, Andrew W.; DiVincenzo, David P.; Terhal, Barbara M. arXiv https://doi.org/10.48550/arXiv.0711.1556	text	January 2007
Quantum-Inspired Algorithm for the Factorized Form of Unitary Coupled Cluster Theory Chen, Jia; Cheng, Hai-Ping; Freericks, James K. Journal of Chemical Theory and Computation, Vol. 17, Issue 2 https://doi.org/10.1021/acs.jctc.0c01052	journal	January 2021
Observing Topological Invariants Using Quantum Walks in Superconducting Circuits Flurin, E.; Ramasesh, V. V.; Hacohen-Gourgy, S. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031023	journal	August 2017
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23879	journal	September 2017
Quantum Criticality of Quasi-One-Dimensional Topological Anderson Insulators Altland, Alexander; Bagrets, Dmitry; Fritz, Lars Physical Review Letters, Vol. 112, Issue 20 https://doi.org/10.1103/PhysRevLett.112.206602	journal	May 2014
Digital Simulation of Topological Matter on Programmable Quantum Processors Mei, Feng; Guo, Qihao; Yu, Ya-Fei Physical Review Letters, Vol. 125, Issue 16 https://doi.org/10.1103/PhysRevLett.125.160503	journal	October 2020
Disorder-Induced Topological State Transition in Photonic Metamaterials Liu, Changxu; Gao, Wenlong; Yang, Biao Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.183901	journal	November 2017
Error mitigation extends the computational reach of a noisy quantum processor Kandala, Abhinav; Temme, Kristan; Córcoles, Antonio D. Nature, Vol. 567, Issue 7749 https://doi.org/10.1038/s41586-019-1040-7	journal	March 2019
Scalable Quantum Simulation of Molecular Energies O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031007	journal	July 2016
Exactly Solvable Model of Correlated Lattice Electrons in Any Dimensions Hatsugai, Yasuhiro; Kohmoto, Mahito Journal of the Physical Society of Japan, Vol. 61, Issue 6 https://doi.org/10.1143/JPSJ.61.2056	journal	June 1992
AIII and BDI topological systems at strong disorder Song, Juntao; Prodan, Emil Physical Review B, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevB.89.224203	journal	June 2014
An adaptive variational algorithm for exact molecular simulations on a quantum computer Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10988-2	journal	July 2019
Qiskit: An Open-source Framework for Quantum Computing Aleksandrowicz, Gadi; Alexander, Thomas; Barkoutsos, Panagiotis https://doi.org/10.5281/zenodo.2562111	software	January 2019

Similar Records

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Journal Article · 2021 · Quantum · OSTI ID:2234346

Xiao, Xiao; Freericks, J. K.; Kemper, A. F.

Noise robust detection of quantum phase transitions

Journal Article · 2024 · Physical Review Research · OSTI ID:2480749

Lively, Kevin; Bode, Tim; Szangolies, Jochen; +2 more

Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers

Conference · 2023 · OSTI ID:2480055

Wang, Yan

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

Title: Robust measurement of wave function topology on NISQ quantum computers

Citation Formats

References (63)

Similar Records

Related Subjects