Analogue Quantum Simulation with Fixed-Frequency Transmon Qubits

Sean Greenaway1, Adam Smith2,3, Florian Mintert1,4, and Daniel Malz5,6

1Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom
2School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
3Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK
4Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
5Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
6Department of Physics, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany

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


We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.

► BibTeX data

► References

[1] Leonid V. Abdurakhimov, Imran Mahboob, Hiraku Toida, Kosuke Kakuyanagi, Yuichiro Matsuzaki, and Shiro Saito. Identification of different types of high-frequency defects in superconducting qubits. PRX Quantum, 3: 040332, Dec 2022. 10.1103/​PRXQuantum.3.040332. URL 10.1103/​PRXQuantum.3.040332.

[2] MD SAJID ANIS, Abby-Mitchell, Héctor Abraham, AduOffei, Rochisha Agarwal, Gabriele Agliardi, Merav Aharoni, Vishnu Ajith, Ismail Yunus Akhalwaya, Gadi Aleksandrowicz, et al. Qiskit experiments, available at​qiskit/​qiskit-experiments. URL https:/​/​​Qiskit/​qiskit-experiments.git.

[3] MD SAJID ANIS, Abby-Mitchell, Héctor Abraham, AduOffei, Rochisha Agarwal, Gabriele Agliardi, Merav Aharoni, Vishnu Ajith, Ismail Yunus Akhalwaya, Gadi Aleksandrowicz, et al. Qiskit: An open-source framework for quantum computing, 2021.

[4] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, 2019. 10.1038/​s41586-019-1666-5.

[5] Rami Barends, Alireza Shabani, Lucas Lamata, Julian Kelly, Antonio Mezzacapo, U Las Heras, Ryan Babbush, Austin G Fowler, Brooks Campbell, Yu Chen, et al. Digitized adiabatic quantum computing with a superconducting circuit. Nature, 534 (7606): 222–226, 2016. 10.1038/​nature17658.

[6] Alexandre Blais, Steven M Girvin, and William D Oliver. Quantum information processing and quantum optics with circuit quantum electrodynamics. Nat. Phys., 16 (3): 247–256, 2020. 10.1038/​s41567-020-0806-z.

[7] Rainer Blatt and Christian F Roos. Quantum simulations with trapped ions. Nat. Phys., 8 (4): 277–284, 2012. 10.1038/​nphys2252.

[8] Antoine Browaeys and Thierry Lahaye. Many-body physics with individually controlled Rydberg atoms. Nat. Phys., 16 (2): 132–142, 2020. 10.1038/​s41567-019-0733-z.

[9] Jerry M Chow, Antonio D Córcoles, Jay M Gambetta, Chad Rigetti, Blake R Johnson, John A Smolin, Jim R Rozen, George A Keefe, Mary B Rothwell, Mark B Ketchen, et al. Simple all-microwave entangling gate for fixed-frequency superconducting qubits. Phys. Rev. Lett., 107 (8): 080502, 2011. 10.1103/​PhysRevLett.107.080502.

[10] J Ignacio Cirac and Peter Zoller. Goals and opportunities in quantum simulation. Nat. Phys., 8 (4): 264–266, 2012. 10.1038/​nphys2275.

[11] SE de Graaf, L Faoro, LB Ioffe, S Mahashabde, JJ Burnett, T Lindström, SE Kubatkin, AV Danilov, and A Ya Tzalenchuk. Two-level systems in superconducting quantum devices due to trapped quasiparticles. Sci. Adv., 6 (51): eabc5055, 2020. 10.1126/​sciadv.abc5055.

[12] David P DiVincenzo. The physical implementation of quantum computation. Fortschr. Phys., 48 (9-11): 771–783, 2000. 10.1002/​1521-3978(200009)48:9/​11<771::AID-PROP771>3.0.CO;2-E.

[13] Yuqian Dong, Yong Li, Wen Zheng, Yu Zhang, Zhuang Ma, Xinsheng Tan, and Yang Yu. Measurement of quasiparticle diffusion in a superconducting transmon qubit. Appl. Sci., 12 (17): 8461, 2022. 10.3390/​app12178461.

[14] Manuel Endres, Marc Cheneau, Takeshi Fukuhara, Christof Weitenberg, Peter Schauss, Christian Gross, Leonardo Mazza, Mari Carmen Banuls, L Pollet, Immanuel Bloch, et al. Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science, 334 (6053): 200–203, 2011. 10.1126/​science.1209284.

[15] Iulia M Georgescu, Sahel Ashhab, and Franco Nori. Quantum simulation. Rev. Mod. Phys., 86 (1): 153, 2014. 10.1103/​RevModPhys.86.153.

[16] Daniel Greif, Thomas Uehlinger, Gregor Jotzu, Leticia Tarruell, and Tilman Esslinger. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science, 340 (6138): 1307–1310, 2013. 10.1126/​science.1236362.

[17] Markus Greiner, Olaf Mandel, Tilman Esslinger, Theodor W Hänsch, and Immanuel Bloch. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature, 415 (6867): 39–44, 2002. 10.1038/​415039a.

[18] Michael J Hartmann. Quantum simulation with interacting photons. J. Opt., 18 (10): 104005, 2016. 10.1088/​2040-8978/​18/​10/​104005.

[19] Michael J Hartmann, Fernando GSL Brandao, and Martin B Plenio. Quantum many-body phenomena in coupled cavity arrays. Laser Photonics Rev., 2 (6): 527–556, 2008. 10.1002/​lpor.200810046.

[20] Andrew A Houck, Hakan E Türeci, and Jens Koch. On-chip quantum simulation with superconducting circuits. Nat. Phys., 8 (4): 292–299, 2012. 10.1038/​nphys2251.

[21] Manik Kapil, Bikash K Behera, and Prasanta K Panigrahi. Quantum simulation of Klein Gordon equation and observation of klein paradox in IBM quantum computer. arXiv preprint arXiv:1807.00521, 2018. 10.48550/​arXiv.1807.00521.

[22] Daniel Koch, Brett Martin, Saahil Patel, Laura Wessing, and Paul M Alsing. Demonstrating NISQ era challenges in algorithm design on IBM's 20 qubit quantum computer. AIP Adv., 10 (9): 095101, 2020. 10.1063/​5.0015526.

[23] Philip Krantz, Morten Kjaergaard, Fei Yan, Terry P Orlando, Simon Gustavsson, and William D Oliver. A quantum engineer's guide to superconducting qubits. Appl. Phys. Rev., 6 (2): 021318, 2019. 10.1063/​1.5089550.

[24] Ben P Lanyon, Cornelius Hempel, Daniel Nigg, Markus Müller, Rene Gerritsma, F Zähringer, Philipp Schindler, Julio T Barreiro, Markus Rambach, Gerhard Kirchmair, et al. Universal digital quantum simulation with trapped ions. Science, 334 (6052): 57–61, 2011. 10.1126/​science.1208001.

[25] Zhi Li, Liujun Zou, and Timothy H Hsieh. Hamiltonian tomography via quantum quench. Phys. Rev. Lett., 124 (16): 160502, 2020. 10.1103/​PhysRevLett.124.160502.

[26] Jin Lin, Fu-Tian Liang, Yu Xu, Li-Hua Sun, Cheng Guo, Sheng-Kai Liao, and Cheng-Zhi Peng. Scalable and customizable arbitrary waveform generator for superconducting quantum computing. AIP Adv., 9 (11): 115309, 2019. 10.1063/​1.5120299.

[27] Jürgen Lisenfeld, Grigorij J Grabovskij, Clemens Müller, Jared H Cole, Georg Weiss, and Alexey V Ustinov. Observation of directly interacting coherent two-level systems in an amorphous material. Nat. Commun., 6 (1): 1–6, 2015. 10.1038/​ncomms7182.

[28] Seth Lloyd. Universal quantum simulators. Science, 273 (5278): 1073–1078, 1996. 10.1126/​science.273.5278.1073.

[29] Ruichao Ma, Clai Owens, Aman LaChapelle, David I Schuster, and Jonathan Simon. Hamiltonian tomography of photonic lattices. Phys. Rev. A, 95 (6): 062120, 2017. 10.1103/​PhysRevA.95.062120.

[30] Moein Malekakhlagh, Easwar Magesan, and David C McKay. First-principles analysis of cross-resonance gate operation. Phys. Rev. A, 102 (4): 042605, 2020. 10.1103/​PhysRevA.102.042605.

[31] Daniel Malz and Adam Smith. Topological two-dimensional Floquet lattice on a single superconducting qubit. Phys. Rev. Lett., 126 (16): 163602, 2021. 10.1103/​PhysRevLett.126.163602.

[32] Matt McEwen, Lara Faoro, Kunal Arya, Andrew Dunsworth, Trent Huang, Seon Kim, Brian Burkett, Austin Fowler, Frank Arute, Joseph C Bardin, et al. Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits. Nat. Phys., 18 (1): 107–111, 2022. 10.1038/​s41567-021-01432-8.

[33] M Müller, Klemens Hammerer, YL Zhou, Christian F Roos, and P Zoller. Simulating open quantum systems: From many-body interactions to stabilizer pumping. New Journal of Physics, 13 (8): 085007, 2011. 10.1088/​1367-2630/​13/​8/​085007.

[34] Nicola Pancotti, Giacomo Giudice, J Ignacio Cirac, Juan P Garrahan, and Mari Carmen Banuls. Quantum East model: Localization, nonthermal eigenstates, and slow dynamics. Phys. Rev. X, 10 (2): 021051, 2020. 10.1103/​PhysRevX.10.021051.

[35] Xinhua Peng, Jiangfeng Du, and Dieter Suter. Quantum phase transition of ground-state entanglement in a heisenberg spin chain simulated in an NMR quantum computer. Phys. Rev. A, 71 (1): 012307, 2005. 10.1103/​PhysRevA.71.012307.

[36] John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2: 79, 2018. 10.22331/​q-2018-08-06-79.

[37] Chad Rigetti and Michel Devoret. Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies. Phys. Rev. B, 81 (13): 134507, 2010. 10.1103/​PhysRevB.81.134507.

[38] Pedram Roushan, Charles Neill, J Tangpanitanon, Victor M Bastidas, A Megrant, Rami Barends, Yu Chen, Z Chen, B Chiaro, A Dunsworth, et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science, 358 (6367): 1175–1179, 2017. 10.1126/​science.aao1401.

[39] Sarah Sheldon, Easwar Magesan, Jerry M Chow, and Jay M Gambetta. Procedure for systematically tuning up cross-talk in the cross-resonance gate. Phys. Rev. A, 93 (6): 060302(R), 2016. 10.1103/​PhysRevA.93.060302.

[40] Adam Smith, MS Kim, Frank Pollmann, and Johannes Knolle. Simulating quantum many-body dynamics on a current digital quantum computer. npj Quantum Inf., 5 (1): 1–13, 2019. 10.1038/​s41534-019-0217-0.

[41] Vinay Tripathi, Mostafa Khezri, and Alexander N Korotkov. Operation and intrinsic error budget of a two-qubit cross-resonance gate. Phys. Rev. A, 100 (1): 012301, 2019. 10.1103/​PhysRevA.100.012301.

[42] Hale F Trotter. On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10 (4): 545–551, 1959. 10.2307/​2033649.

[43] Joseph Vovrosh and Johannes Knolle. Confinement and entanglement dynamics on a digital quantum computer. Sci. Rep., 11 (1): 1–8, 2021. 10.1038/​s41598-021-90849-5.

[44] Joseph Vovrosh, Kiran E Khosla, Sean Greenaway, Christopher Self, Myungshik S Kim, and Johannes Knolle. Simple mitigation of global depolarizing errors in quantum simulations. Phys. Rev. E, 104 (3): 035309, 2021. 10.1103/​PhysRevE.104.035309.

[45] Sheng-Tao Wang, Dong-Ling Deng, and Lu-Ming Duan. Hamiltonian tomography for quantum many-body systems with arbitrary couplings. New J. Phys., 17 (9): 093017, 2015. 10.1088/​1367-2630/​17/​9/​093017.

[46] Samuel A Wilkinson and Michael J Hartmann. Superconducting quantum many-body circuits for quantum simulation and computing. Appl. Phys. Lett., 116 (23): 230501, 2020. 10.1063/​5.0008202.

[47] Xinyuan You, Ziwen Huang, Ugur Alyanak, Alexander Romanenko, Anna Grassellino, and Shaojiang Zhu. Stabilizing and Improving Qubit Coherence by Engineering the Noise Spectrum of Two-Level Systems. Phys. Rev. Applied, 18 (4): 044026, 2022. 10.1103/​PhysRevApplied.18.044026.

[48] Qingling Zhu, Zheng-Hang Sun, Ming Gong, Fusheng Chen, Yu-Ran Zhang, Yulin Wu, Yangsen Ye, Chen Zha, Shaowei Li, Shaojun Guo, et al. Observation of thermalization and information scrambling in a superconducting quantum processor. Phys. Rev. Lett., 128 (16): 160502, 2022. 10.1103/​PhysRevLett.128.160502.

Cited by

[1] Naoki Kanazawa, Daniel Egger, Yael Ben-Haim, Helena Zhang, William Shanks, Gadi Aleksandrowicz, and Christopher Wood, "Qiskit Experiments: A Python package to characterize and calibrate quantum computers", The Journal of Open Source Software 8 84, 5329 (2023).

[2] Yuxiang Peng, Jacob Young, Pengyu Liu, and Xiaodi Wu, "SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation", arXiv:2303.02775, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-04-12 10:07:18). 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 2024-04-12 10:07:17).