Nonadiabatic geometric quantum computation with optimal control on superconducting circuits
Jing Xu1, Sai Li1, Tao Chen1, Zheng-Yuan Xue1,2()
1. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China 2. Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric quantum computation scheme on superconducting circuits to engineer arbitrary quantum gates, which share both the robust merit of geometric phases and the capacity to combine with optimal control technique to further enhance the gate robustness. Specifically, in our proposal, arbitrary geometric single-qubit gates can be realized on a transmon qubit, by a resonant microwave field driving, with both the amplitude and phase of the driving being timedependent. Meanwhile, nontrivial two-qubit geometric gates can be implemented by two capacitively coupled transmon qubits, with one of the transmon qubits’ frequency being modulated to obtain effective resonant coupling between them. Therefore, our scheme provides a promising step towards fault-tolerant solid-state quantum computation.
P. Solinas, P. Zanardi, and N. Zanghì,Robustness of non-Abelian holonomic quantum gates against parametric noise, Phys. Rev. A 70(4), 042316 (2004) https://doi.org/10.1103/PhysRevA.70.042316
5
S.-L. Zhu and P. Zanardi, Geometric quantum gates that are robust against stochastic control errors, Phys. Rev. A 72, 020301(R) (2005) https://doi.org/10.1103/PhysRevA.72.020301
M. Johansson, E. Sjöqvist, L. M. Andersson, M. Ericsson, B. Hessmo, K. Singh, and D. M. Tong, Robustness of nonadiabatic holonomic gates, Phys. Rev. A 86(6), 062322 (2012) https://doi.org/10.1103/PhysRevA.86.062322
S. L. Zhu and Z. D. Wang, Implementation of universal quantum gates based on nonadiabatic geometric phases, Phys. Rev. Lett. 89(9), 097902 (2002) https://doi.org/10.1103/PhysRevLett.89.097902
10
P. Z. Zhao, X. D. Cui, G. F. Xu, E. Sjöqvist, and D. M. Tong, Rydberg-atom-based scheme of nonadiabatic geometric quantum computation, Phys. Rev. A 96(5), 052316 (2017) https://doi.org/10.1103/PhysRevA.96.052316
X. Y. Chen, T. Li, and Z. Q. Yin, Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin, Sci. Bull. 64(6), 380 (2019) https://doi.org/10.1016/j.scib.2019.02.018
13
T. Bækkegaard, L. B. Kristensen, N. J. S. Loft, C. K. Andersen, D. Petrosyan, and N. T. Zinner, Realization of efficient quantum gates with a superconducting qubitqutrit circuit, Sci. Rep. 9(1), 13389 (2019) https://doi.org/10.1038/s41598-019-49657-1
14
E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, Non-adiabatic holonomic quantum computation, New J. Phys. 14(10), 103035 (2012) https://doi.org/10.1088/1367-2630/14/10/103035
15
G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, Nonadiabatic holonomic quantum computation in decoherencefree subspaces, Phys. Rev. Lett. 109(17), 170501 (2012) https://doi.org/10.1103/PhysRevLett.109.170501
16
G. Falci, R. Fazio, G. M. Palma, J. Siewert, and V. Vedral, Detection of geometric phases in superconducting nanocircuits, Nature 407(6802), 355 (2000) https://doi.org/10.1038/35030052
17
D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate, Nature 422(6930), 412 (2003) https://doi.org/10.1038/nature01492
18
P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Goppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraff, Observation of Berry’s phase in a solid-state qubit, Science 318(5858), 1889 (2007) https://doi.org/10.1126/science.1149858
19
J. M. Cui, M. Z. Ai, R. He, Z. H. Qian, X. K. Qin, Y. F. Huang, Z. W. Zhou, C. F. Li, T. Tu, and G. C. Guo, Experimental demonstration of suppressing residual geometric dephasing, Sci. Bull. 64(23), 1757 (2019) https://doi.org/10.1016/j.scib.2019.09.007
20
J. Chu, D. Li, X. Yang, S. Song, Z. Han, Z. Yang, Y. Dong, W. Zheng, Z. Wang, X. Yu, D. Lan, X. Tan, and Y. Yu, Realization of superadiabatic two-qubit gates using parametric modulation in superconducting circuits, Phys. Rev. Appl. 13(6), 064012 (2020) https://doi.org/10.1103/PhysRevApplied.13.064012
21
Y. Xu, Z. Hua, T. Chen, X. Pan, X. Li, J. Han, W. Cai, Y. Ma, H. Wang, Y. P. Song, Z. Y. Xue, and L. Sun, Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit, Phys. Rev. Lett. 124(23), 230503 (2020) https://doi.org/10.1103/PhysRevLett.124.230503
22
P. Z. Zhao, Z. Dong, Z. Zhang, G. Guo, D. M. Tong, and Y. Yin, Experimental realization of nonadiabatic geometric gates with a superconducting Xmon qubit, arXiv: 1909.09970 (2019)
23
S. B. Zheng, C. P. Yang, and F. Nori, Comparison of the sensitivity to systematic errors between nonadiabatic non-Abelian geometric gates and their dynamical counterparts, Phys. Rev. A 93(3), 032313 (2016) https://doi.org/10.1103/PhysRevA.93.032313
24
J. Jing, C. H. Lam, and L. A. Wu, Non-Abelian holonomic transformation in the presence of classical noise, Phys. Rev. A 95(1), 012334 (2017) https://doi.org/10.1103/PhysRevA.95.012334
25
B. J. Liu, X. K. Song, Z. Y. Xue, X. Wang, and M. H. Yung, Plug-and-play approach to nonadiabatic geometric quantum gates, Phys. Rev. Lett. 123(10), 100501 (2019) https://doi.org/10.1103/PhysRevLett.123.100501
26
S. Li, T. Chen, and Z. Y. Xue, Fast holonomic quantum computation on superconducting circuits with optimal control, Adv. Quantum Technol. 3(3), 2000001 (2020) https://doi.org/10.1002/qute.202000001
27
T. Yan, B. J. Liu, K. Xu, C. Song, S. Liu, Z. Zhang, H. Deng, Z. Yan, H. Rong, K. Huang, M. H. Yung, Y. Chen, and D. Yu, Experimental realization of nonadiabatic shortcut to non-Abelian geometric gates, Phys. Rev. Lett. 122(8), 080501 (2019) https://doi.org/10.1103/PhysRevLett.122.080501
28
M.-Z. Ai, S. Li, Z. Hou, R. He, Z.-H. Qian, Z.-Y. Xue, J.-M. Cui, Y.-F. Huang, C.-F. Li, and G.-C. Guo, Experimental realization of nonadiabatic holonomic singlequbit quantum gates with optimal control in a trapped ion, arXiv: 2006.04609 (2020)
29
A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, Optimally robust shortcuts to population inversion in two-level quantum systems, New J. Phys. 14(9), 093040 (2012) https://doi.org/10.1088/1367-2630/14/9/093040
30
D. Daems, A. Ruschhaupt, D. Sugny, and S. Gu�rin, Robust quantum control by a single-shot shaped pulse, Phys. Rev. Lett. 111(5), 050404 (2013) https://doi.org/10.1103/PhysRevLett.111.050404
31
M. H. Goerz, F. Motzoi, K. B. Whaley, and C. P. Koch, Charting the circuit QED design landscape using optimal control theory, npj Quantum Inf. 3, 37 (2017) https://doi.org/10.1038/s41534-017-0036-0
32
G. Bhole and J. A. Jones, Practical pulse engineering: Gradient ascent without matrix exponentiation, Front. Phys. 13(3), 130312 (2018) https://doi.org/10.1007/s11467-018-0791-1
33
G. Long, G. Feng, and P. Sprenger, Overcoming synthesizer phase noise in quantum sensing, Quantum Engineering 1(4), e27 (2019) https://doi.org/10.1002/que2.27
34
K. Li, Eliminating the noise from quantum computing hardware, Quantum Engineering 2(1), e28 (2020) https://doi.org/10.1002/que2.28
35
J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011) https://doi.org/10.1038/nature10122
36
M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339(6124), 1169 (2013) https://doi.org/10.1126/science.1231930
37
X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718–719, 1 (2017) https://doi.org/10.1016/j.physrep.2017.10.002
38
M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I. J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11(1), 369 (2020) https://doi.org/10.1146/annurev-conmatphys-031119-050605
39
Y. J. Fan, Z. F. Zheng, Y. Zhang, D. M. Lu, and C. P. Yang, One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED, Front. Phys. 14(2), 21602 (2019) https://doi.org/10.1007/s11467-018-0875-y
40
X. T. Mo and Z. Y. Xue, Single-step multipartite entangled states generation from coupled circuit cavities, Front. Phys. 14(3), 31602 (2019) https://doi.org/10.1007/s11467-019-0888-1
J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator, Phys. Rev. A 83(1), 012308 (2011) https://doi.org/10.1103/PhysRevA.83.012308
43
T. H. Wang, Z. X. Zhang, L. Xiang, Z. H. Gong, J. L. Wu, and Y. Yin, Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories, Sci. China Phys. Mech. Astron. 61(4), 047411 (2018) https://doi.org/10.1007/s11433-017-9156-1
44
T. H. Wang, Z. X. Zhang, L. Xiang, Z. L. Jia, P. Duan, W. Z. Cai, Z. H. Gong, Z. W. Zong, M. M. Wu, J. L. Wu, L. Y. Sun, Y. Yin, and G. P. Guo, The experimental realization of highfidelity “shortcut-to-adiabaticity” quantum gates in a superconducting Xmon qubit, New J. Phys. 20(6), 065003 (2018) https://doi.org/10.1088/1367-2630/aac9e7
45
F. W. Strauch, P. R. Johnson, A. J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood, Quantum logic gates for coupled superconducting phase qubits, Phys. Rev. Lett. 91(16), 167005 (2003) https://doi.org/10.1103/PhysRevLett.91.167005
46
L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Preparation and measurement of three-qubit entanglement in a superconducting circuit, Nature 467(7315), 574 (2010) https://doi.org/10.1038/nature09416
47
M. Reagor, C. B. Osborn, N. Tezak, A. Staley, G. Prawiroatmodjo, et al., Demonstration of universal parametric entangling gates on a multi-qubit lattice, Sci. Adv. 4(2), eaao3603 (2018) https://doi.org/10.1126/sciadv.aao3603
48
S. A. Caldwell, N. Didier, C. A. Ryan, E. A. Sete, A. Hudson, et al., Parametrically activated entangling gates using transmon qubits, Phys. Rev. Appl. 10(3), 034050 (2018)
49
X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z. Y. Xue, Z. Yin, and L. Sun, Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings, Phys. Rev. Appl. 10(5), 054009 (2018) https://doi.org/10.1103/PhysRevApplied.10.054009
