Simulation of the influence of imperfections on dynamical decoupling of a superconducting qubit
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摘要
Dynamical decoupling is widely used in many quantum computing systems to combat decoherence. In a practical superconducting quantum system, imperfections can plague decoupling performance. In this work, imperfections in a superconducting qubit and its control system are modeled via modified Hamiltonian and collapse operator. A master equation simulation is carried out on the qubit under 1/f environment noise spectrum. The average dephasing rate of qubit is extracted to characterize the impact of different imperfections on the decoupling from dephasing. We find that the precision of pulse position, on–off ratio, and filtering effect are most critical. Bounded pulses have weaker impact,while variation in pulse width and qubit relaxation are insignificant. Consequently, alternative decoupling protocols, jitter mitigation, cascaded mixers, and pulse shaping can be conducive to the performance of decoupling. This work may assist the analysis and optimization of dynamical decoupling on noisy superconducting quantum systems.
Dynamical decoupling is widely used in many quantum computing systems to combat decoherence. In a practical superconducting quantum system, imperfections can plague decoupling performance. In this work, imperfections in a superconducting qubit and its control system are modeled via modified Hamiltonian and collapse operator. A master equation simulation is carried out on the qubit under 1/f environment noise spectrum. The average dephasing rate of qubit is extracted to characterize the impact of different imperfections on the decoupling from dephasing. We find that the precision of pulse position, on–off ratio, and filtering effect are most critical. Bounded pulses have weaker impact,while variation in pulse width and qubit relaxation are insignificant. Consequently, alternative decoupling protocols, jitter mitigation, cascaded mixers, and pulse shaping can be conducive to the performance of decoupling. This work may assist the analysis and optimization of dynamical decoupling on noisy superconducting quantum systems.
Dynamical decoupling is widely used in many quantum computing systems to combat decoherence. In a practical superconducting quantum system, imperfections can plague decoupling performance. In this work, imperfections in a superconducting qubit and its control system are modeled via modified Hamiltonian and collapse operator. A master equation simulation is carried out on the qubit under 1/f environment noise spectrum. The average dephasing rate of qubit is extracted to characterize the impact of different imperfections on the decoupling from dephasing. We find that the precision of pulse position, on–off ratio, and filtering effect are most critical. Bounded pulses have weaker impact,while variation in pulse width and qubit relaxation are insignificant. Consequently, alternative decoupling protocols, jitter mitigation, cascaded mixers, and pulse shaping can be conducive to the performance of decoupling. This work may assist the analysis and optimization of dynamical decoupling on noisy superconducting quantum systems.
引文
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[2] Hu L, Ma Y W, Cai W Z, Mu X H, Xu Y, Wang W T, Wu Y K, Wang H Y, Song Y P, Zou C L, Girvin S M, Duan L M and Sun L Y 2018arXiv:1805.09072[quant-ph]
[3] Lidar D A 2014 Quantum Information and Computation for Chemistry(Chichester:John Wiley and Sons)p. 295
[4] Zhang Z R, Li C Y, Wu C W, Dai H Y and Li C Z 2012 Phys. Rev. A 86042320
[5] Li J and Paraoanu G S 2012 J. Phys.:Conf. Ser. 338 012010
[6] Takita M, Corcoles AD, Magesan E, Abdo B, Brink M, Cross A, Chow J M and Gambetta J M 2016 Phys. Rev. Lett. 117 210505
[7] Neill C, Roushan P, Kechedzhi K, et al. 2018 Science 360 195
[8] Ng H K, Lidar D A and Preskill J 2011 Phys. Rev. A 84 012305
[9] Pan Y, Xi Z R and Cui W 2012 Chin. Sci. Bull. 57 2228
[10] Wang D M, Qian Y, Xu J B and Yu Y H 2015 Chin. Phys. B 24 110304
[11] Guo Q J, Zheng S B, Wang J W, Song C, Zhang P F, Li K M, Liu W X,Deng H, Huang K Q, Zheng D N, Zhu X B, Wang H, Lu C Y and Pan J W 2018 Phys. Rev. Lett. 121 130501
[12] Pokharel B, Anand N, Fortma B and Lidar D A 2018 Phys. Rev. Lett.121 220502
[13] Gustavsson S, Yan F, Bylander J, Yoshihara F, Nakamura Y, Orlando T P and Oliver W D 2012 Phys. Rev. Lett. 109 010502
[14] Bylander J, Gustavsson S, Yan F, Yoshihara F, Harrabi K, Fitch G, Cory D G, Nakamura Y, Tsai J S and Oliver W D 2011 Nat. Phys. 7 565
[15] Chu Y, Axline C, Wang C, Brecht T, Gao Y Y, Frunzio L and Schoelkopf R J 2016 Appl. Phys. Lett. 109 112601
[16] He L Z, Zhang M C, Wu C W, Xie Y, Wu W and Chen P X 2018 Chin.Phys. B 27 120303
[17] Sakurai J J and Napolitano J 2014 Modern Quantum Mechanics, 2nd edn.(Pearson)p. 185
[18] Beaudoin F 2016"Understanding and Suppressing Dephasing Noise in Semiconductor Qubits,"Ph. D. Dissertation(McGill University)
[19] Paladino E, Galperin Y M, Falci G and Altshuler B L 2014 Rev. Mod.Phys. 86 361
[20] Lindblad G 1976 Commun. Math. Phys. 48 119
[21] Lidar D A and Brun T A 2013 Quantum Error Correction(Cambridge University Press)p. 8
[22] Viola L and Knill E 2003 Phys. Rev. Lett. 90 037901
[23] Carr H Y and Purcell E M 1954 Phys. Rev. 94 630
[24] Meiboom S and Gill D 1958 Rev. Sci. Instrum. 29 688
[25] Borneman T W, Hiirlimann M D and Cory D G 2010 J. Magn. Reson.207 220
[26] Uhrig G S 2007 Phys. Rev. Lett. 98 100504
[27] Souza A M, lvarez G A and Suter D 2012 Phil. Trans. R. Soc. A 3704748
[28] Johansson J R, Nation P D and Nori F 2012 Comput. Phys. Commun.183 1760
[29] Chen Z J 2018"Metrology of Quantum Control and Measurement in Superconducting Qubits", Ph. D. Dissertation(University of California, Santa Barbara)
[30] Wocjan P 2006 Phys.Rev. A 73 062317
[31] Khodjasteh K and Lidar D A 2005 Phys. Rev. Lett. 95 180501
[32] Pham L M, Bar-Gill N, Belthangady C, Le Sage D, Cappellaro P, Lukin M D, Yacoby A and Walsworth R L 2012 Phys. Rev. B 86 045214
[2] Hu L, Ma Y W, Cai W Z, Mu X H, Xu Y, Wang W T, Wu Y K, Wang H Y, Song Y P, Zou C L, Girvin S M, Duan L M and Sun L Y 2018arXiv:1805.09072[quant-ph]
[3] Lidar D A 2014 Quantum Information and Computation for Chemistry(Chichester:John Wiley and Sons)p. 295
[4] Zhang Z R, Li C Y, Wu C W, Dai H Y and Li C Z 2012 Phys. Rev. A 86042320
[5] Li J and Paraoanu G S 2012 J. Phys.:Conf. Ser. 338 012010
[6] Takita M, Corcoles AD, Magesan E, Abdo B, Brink M, Cross A, Chow J M and Gambetta J M 2016 Phys. Rev. Lett. 117 210505
[7] Neill C, Roushan P, Kechedzhi K, et al. 2018 Science 360 195
[8] Ng H K, Lidar D A and Preskill J 2011 Phys. Rev. A 84 012305
[9] Pan Y, Xi Z R and Cui W 2012 Chin. Sci. Bull. 57 2228
[10] Wang D M, Qian Y, Xu J B and Yu Y H 2015 Chin. Phys. B 24 110304
[11] Guo Q J, Zheng S B, Wang J W, Song C, Zhang P F, Li K M, Liu W X,Deng H, Huang K Q, Zheng D N, Zhu X B, Wang H, Lu C Y and Pan J W 2018 Phys. Rev. Lett. 121 130501
[12] Pokharel B, Anand N, Fortma B and Lidar D A 2018 Phys. Rev. Lett.121 220502
[13] Gustavsson S, Yan F, Bylander J, Yoshihara F, Nakamura Y, Orlando T P and Oliver W D 2012 Phys. Rev. Lett. 109 010502
[14] Bylander J, Gustavsson S, Yan F, Yoshihara F, Harrabi K, Fitch G, Cory D G, Nakamura Y, Tsai J S and Oliver W D 2011 Nat. Phys. 7 565
[15] Chu Y, Axline C, Wang C, Brecht T, Gao Y Y, Frunzio L and Schoelkopf R J 2016 Appl. Phys. Lett. 109 112601
[16] He L Z, Zhang M C, Wu C W, Xie Y, Wu W and Chen P X 2018 Chin.Phys. B 27 120303
[17] Sakurai J J and Napolitano J 2014 Modern Quantum Mechanics, 2nd edn.(Pearson)p. 185
[18] Beaudoin F 2016"Understanding and Suppressing Dephasing Noise in Semiconductor Qubits,"Ph. D. Dissertation(McGill University)
[19] Paladino E, Galperin Y M, Falci G and Altshuler B L 2014 Rev. Mod.Phys. 86 361
[20] Lindblad G 1976 Commun. Math. Phys. 48 119
[21] Lidar D A and Brun T A 2013 Quantum Error Correction(Cambridge University Press)p. 8
[22] Viola L and Knill E 2003 Phys. Rev. Lett. 90 037901
[23] Carr H Y and Purcell E M 1954 Phys. Rev. 94 630
[24] Meiboom S and Gill D 1958 Rev. Sci. Instrum. 29 688
[25] Borneman T W, Hiirlimann M D and Cory D G 2010 J. Magn. Reson.207 220
[26] Uhrig G S 2007 Phys. Rev. Lett. 98 100504
[27] Souza A M, lvarez G A and Suter D 2012 Phil. Trans. R. Soc. A 3704748
[28] Johansson J R, Nation P D and Nori F 2012 Comput. Phys. Commun.183 1760
[29] Chen Z J 2018"Metrology of Quantum Control and Measurement in Superconducting Qubits", Ph. D. Dissertation(University of California, Santa Barbara)
[30] Wocjan P 2006 Phys.Rev. A 73 062317
[31] Khodjasteh K and Lidar D A 2005 Phys. Rev. Lett. 95 180501
[32] Pham L M, Bar-Gill N, Belthangady C, Le Sage D, Cappellaro P, Lukin M D, Yacoby A and Walsworth R L 2012 Phys. Rev. B 86 045214