Coherent-driving-assisted quantum speedup in Markovian channels

doi:10.1088/1674-1056/abc150

Abstract As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.

Keywords: quantum dynamics control quantum speed limit Markovian dynamics

Received: 22 July 2020
Revised: 08 September 2020
Accepted manuscript online: 15 October 2020

PACS:	03.65.Yz	(Decoherence; open systems; quantum statistical methods)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	42.50.Lc	(Quantum fluctuations, quantum noise, and quantum jumps)

Fund: Project supported by the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2020MA086) and the National Natural Science Foundation of China (Grant Nos. 61675115 and 11974209).

Corresponding Authors: ^†Corresponding author. E-mail: yingjiezhang@qfnu.edu.cn

Cite this article:

Xiang Lu(鹿翔), Ying-Jie Zhang(张英杰), and Yun-Jie Xia(夏云杰) Coherent-driving-assisted quantum speedup in Markovian channels 2021 Chin. Phys. B 30 020301

1 Mandelstam L and Tamm I1945 J. Phys. (USSR) 9 249
2 Fleming G N 1973 Nuovo Cimento A 16 232
3 Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697
4 Vaidman L 1992 Am. J. Phys. 60 182
5 Levitin L B and Toffoli T 2009 Phys. Rev. Lett. 103 160502
6 Giovannetti V, Lloyd S and Maccone L 2003 Phys. Rev. A 67 052109
7 Jones P J and Kok P 2010 Phys. Rev. A 82 022107
8 Zwierz M 2012 Phys. Rev. A 86 016101
9 Deffner S and Lutz E 2013 J. Phys. A 46 335302
10 Pfeifer P 1993 Phys. Rev. Lett. 70 3365
11 Pfeifer P and Fröhlich J 1995 Rev. Mod. Phys. 67 759
12 Taddei M M, Escher B M, Davidovich L and de Matos Filho R L 2013 Phys. Rev. Lett. 110 050402
13 del Campo A, Egusquiza I L, Plenio M B and Huelga S F 2013 Phys. Rev. Lett. 110 050403
14 Deffner S and Lutz E 2013 Phys. Rev. Lett. 111 010402
15 Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2014 Sci. Rep. 4 4890
16 Xu K, Han W, Zhang Y J and Fan H 2018 Chin. Phys. B 27 010302
17 Han W, Jiang K X, Zhang Y J and Xia Y J 2015 Chin. Phys. B 24 120304
18 Xu Z Y, Luo S L, Yang W L, Liu C and Zhu S Q 2014 Phys. Rev. A 89 012307
19 Deffner S 2014 J. Phys. B 47 145502
20 Nielsen M A and Chuang I L2000 Quantum Computation and Quantum Information (New York: Cambridge University Press)
21 Bekenstein J D 1981 Phys. Rev. Lett. 46 623
22 Deffner S and Lutz E 2010 Phys. Rev. Lett. 105 170402
23 Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
24 Mukherjee V, Carlini A, Mari A, Caneva T, Montangero S, Calarco T, Fazio R and Giovannetti V 2013 Phys. Rev. A 88 062326
25 Hegerfeldt G C 2013 Phys. Rev. Lett. 111 260501
26 Hegerfeldt G C 2014 Phys. Rev. A 90 032110
27 Avinadav C, Fischer R, London P and Gershoni D 2014 Phys. Rev. B 89 245311
28 Campaioli F, Pollock F A, Binder F C and Modi K 2018 Phys. Rev. Lett. 120 060409
29 Campaioli F, Pollock F A and Modi K 2019 Quantum 3 168
30 Sun S N and Zheng Y J 2019 Phys. Rev. Lett. 123 180403
31 A quantum information science and technology roadmap, part 1: Quantum computation, Section 6.9, LA-UR-04-1778 (2004)
32 Hughes R, Doolen G, Awschalom D, Caves C, Chapman M, Clark R, Cory D, DiVincenzo D, Ekert A, Hammel P C, Kwiat P, Lloyd S, Milburn G, Orlando T, Steel D, Vazirani U, Whaley K B and Wineland D A Quantum Information Science and Technology Roadmap, Part 1: Quantum Computation (Technical report, Advanced Research and Development Activity (ARDA))
33 Liu C, Xu Z Y and Zhu S Q 2015 Phys. Rev. A 91 022102
34 Wu S X, Zhang Y, Yu C S and Song H S 2015 J. Phys. A 48 045301
35 Bukov M, Sels D and Polkovnikov A 2019 Phys. Rev. X 9 011034
36 Zhang Y J, Han W, Xia Y J, Tian J X and Fan H 2016 Sci. Rep. 6 27349
37 Hamma A, Markopoulou F, Premont-Schwarz I and Severini S 2009 Phys. Rev. Lett. 102 017204
38 Wu S X and Yu C S 2018 Phys. Rev. A 98 042132
39 Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Phys. Rev. A 91 032112
40 Zhang Y J, Han W, Xia Y J, Yu Y M and Fan H 2015 Sci. Rep. 5 13359
41 Cai X J and Zheng Y J 2017 Phys. Rev. A 95 052104
42 Shanahan B, Chenu A, Margolus N and del Campo A 2018 Phys. Rev. Lett. 120 070401
43 Okuyama M and Ohzeki M 2018 Phys. Rev. Lett. 120 070402
44 Liu H B, Yang W L, An J H and Xu Z Y 2016 Phys. Rev. A 93 020105
45 Zhang Y J, Xia Y J and Fan H 2016 Europhys. Lett. 116 30001
46 Xu K, Zhang Y J, Xia Y J, Wang Z D and Fan H 2018 Phys. Rev. A 98 022114
47 Cimmarusti A D, Yan Z, Patterson B D, Corcos L P, Orozco L A and Deffner S 2015 Phys. Rev. Lett. 114 233602
48 Felicetti S, Fedortchenko S, Rossi J R, Ducci S, Favero I, Coudreau T and Milman P 2017 Phys. Rev. A 95 022322
49 Gatto D, De Pasquale A and Giovannetti V 2019 Phys. Rev. A 99 032307
50 Qian Y and Xu J B 2012 Chin. Phys. B 21 030305
51 Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y and Du J F 2015 Nature Commun. 6 8748
52 Huang Y Y, Wu Y K, Wang F, Hou P Y, Wang W B, Zhang W G, Lian W Q, Liu Y Q. Wang H Y, Zhang H Y, He L, Chang X Y, Xu Y and Duan L M 2019 Phys. Rev. Lett. 122 010503
53 Barends R et al. 2014 Nature 508 500
54 Barends R et al. 2016 Nature 534 222
55 Rivas A, Huelga S F and Plenio M B 2014 Rep. Prog. Phys. 77 094001
56 Breuer H P, Laine E M, Piilo J and Vacchini B 2016 Rev. Mod. Phys. 88 021002
57 Breuer H P, Laine E M and Piilo J 2009 Phys. Rev. Lett. 103 210401
58 Gorini V and Kossakowski A 1976 J. Math. Phys. 17 1298
59 Lindblad G 1976 Commun. Math. Phys. 48 119
60 Varcoe B T H, Brattke S, Weidinger M and Walther H 2000 Nature 403 743
61 Jonathan D and Plenio M B 2001 Phys. Rev. Lett. 87 127901
62 You J Q and Nori F 2011 Nature 474 589
63 Prawer S and Greentree A D 2008 Science 320 1601
64 Dai K Z et al. 2017 Appl. Phys. Lett. 111 242601
65 Magazzu1 L et al. 2018 Nat. Commun. 9 1403

[1]	Quantum speed limit of the double quantum dot in pure dephasing environment under measurement Zhenyu Lin(林振宇), Tian Liu(刘天), Zongliang Li(李宗良), Yanhui Zhang(张延惠), and Kang Lan(蓝康). Chin. Phys. B, 2022, 31(7): 070307.
[2]	Quantum speed limit for mixed states in a unitary system Jie-Hui Huang(黄接辉), Li-Guo Qin(秦立国), Guang-Long Chen(陈光龙), Li-Yun Hu(胡利云), and Fu-Yao Liu(刘福窑). Chin. Phys. B, 2022, 31(11): 110307.
[3]	Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots M Bagheri Harouni. Chin. Phys. B, 2021, 30(9): 090301.
[4]	Quantum speed limit for the maximum coherent state under the squeezed environment Kang-Ying Du(杜康英), Ya-Jie Ma(马雅洁), Shao-Xiong Wu(武少雄), and Chang-Shui Yu(于长水). Chin. Phys. B, 2021, 30(9): 090308.
[5]	Margolus-Levitin speed limit across quantum to classical regimes based on trace distance Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水). Chin. Phys. B, 2020, 29(5): 050302.
[6]	Quantum speed limit time of a non-Hermitian two-level system Yan-Yi Wang(王彦懿), Mao-Fa Fang(方卯发). Chin. Phys. B, 2020, 29(3): 030304.
[7]	Quantum speed limit time and entanglement in a non-Markovian evolution of spin qubits of coupled quantum dots M. Bagheri Harouni. Chin. Phys. B, 2020, 29(12): 124203.
[8]	On the time-independent Hamiltonian in real-time and imaginary-time quantum annealing Jie Sun(孙杰)† and Songfeng Lu(路松峰)‡. Chin. Phys. B, 2020, 29(10): 100303.
[9]	Quantum speed-up capacity in different types of quantum channels for two-qubit open systems Wei Wu(吴薇), Xin Liu(刘辛), Chao Wang(王超). Chin. Phys. B, 2018, 27(6): 060302.
[10]	Non-Markovian speedup dynamics control of the damped Jaynes-Cummings model with detuning Kai Xu(徐凯), Wei Han(韩伟), Ying-Jie Zhang(张英杰), Heng Fan(范桁). Chin. Phys. B, 2018, 27(1): 010302.
[11]	Quantum speed limit time of a two-level atom under different quantum feedback control Min Yu(余敏), Mao-Fa Fang(方卯发), Hong-Mei Zou(邹红梅). Chin. Phys. B, 2018, 27(1): 010303.
[12]	Quantum speed limits of a qubit system interacting with a nonequilibrium environment Zhi He(贺志), Chun-Mei Yao(姚春梅), Li Li(李莉), Qiong Wang(王琼). Chin. Phys. B, 2016, 25(8): 080304.
[13]	Quantum speed limits for Bell-diagonal states Han Wei (韩伟), Jiang Ke-Xia (江克侠), Zhang Ying-Jie (张英杰), Xia Yun-Jie (夏云杰). Chin. Phys. B, 2015, 24(12): 120304.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Coherent-driving-assisted quantum speedup in Markovian channels

Cite this article:

Online attention