Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2018 Impact Factor: 2.483

Frontiers of Physics  2019, Vol. 14 Issue (2): 21602   https://doi.org/10.1007/s11467-018-0875-y
  本期目录
One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED
You-Ji Fan1, Zhen-Fei Zheng2, Yu Zhang3, Dao-Ming Lu1, Chui-Ping Yang4,5()
1. College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China
2. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
3. School of Physics, Nanjing University, Nanjing 210093, China
4. Quantum Information Research Center, Shangrao Normal University, Shangrao 334001, China
5. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
 全文: PDF(820 KB)  
Abstract

We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit (cqubit) simultaneously controlling n–1 target cqubits. The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.

Key wordscircuit QED    cat-state    multi-target-qubit controlled phase gate
收稿日期: 2018-09-07      出版日期: 2018-12-29
 引用本文:   
. [J]. Frontiers of Physics, 2019, 14(2): 21602.
You-Ji Fan, Zhen-Fei Zheng, Yu Zhang, Dao-Ming Lu, Chui-Ping Yang. One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED. Front. Phys. , 2019, 14(2): 21602.
 链接本文:  
http://academic.hep.com.cn/fop/CN/10.1007/s11467-018-0875-y
http://academic.hep.com.cn/fop/CN/Y2019/V14/I2/21602
1 D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. Lond. A 400(1818), 97 (1985)
2 P. W. Shor, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science IEEE Computer Society Press, Santa Fe, NM, 1994
3 L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79(2), 325 (1997)
https://doi.org/10.1103/PhysRevLett.79.325
4 A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52(5), 3457 (1995)
https://doi.org/10.1103/PhysRevA.52.3457
5 M. Mötöen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, Quantum circuits for general multiqubit gates, Phys. Rev. Lett. 93(13), 130502 (2004)
https://doi.org/10.1103/PhysRevLett.93.130502
6 Y. Liu, G. L. Long, and Y. Sun, Analytic one-bit and CNOT gate constructions of general n-qubit controlled gates, Int. J. Quant. Inf. 6(03), 447 (2008)
https://doi.org/10.1142/S0219749908003621
7 J. K. Pachos and P. L. Knight, Quantum computation with a one-dimensional optical lattice, Phys. Rev. Lett. 91(10), 107902 (2003)
https://doi.org/10.1103/PhysRevLett.91.107902
8 H. Ollivier and P. Milman, Proposal for realization of a Toffoli gate via cavity-assisted collision, arXiv: quantph/ 0306064 (2003)
9 J. Zhang, W. Liu, Z. Deng, Z. Lu, and G. L. Long, Modularization of multi-qubit controlled phase gate and its NMR implementation, J. Opt. B 7, 22 (2005)
https://doi.org/10.1088/1464-4266/7/1/005
10 A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481(7380), 170 (2012)
https://doi.org/10.1038/nature10713
11 L. M. Duan, B. Wang, and H. J. Kimble, Robust quantum gates on neutral atoms with cavity-assisted photonscattering,Phys. Rev. A 72(3), 032333 (2005)
https://doi.org/10.1103/PhysRevA.72.032333
12 X. Wang, A. Sørensen, and K. Mølmeret, Multibit gates for quantum computing, Phys. Rev. Lett. 86(17), 3907 (2001)
https://doi.org/10.1103/PhysRevLett.86.3907
13 X. Zou, Y. Dong, and G. C. Guo, Implementing a conditional zgate by a combination of resonant interaction and quantum interference, Phys. Rev. A 74(3), 032325 (2006)
https://doi.org/10.1103/PhysRevA.74.032325
14 C. P. Yang and S. Han, n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator, Phys. Rev. A 72(3), 032311 (2005)
https://doi.org/10.1103/PhysRevA.72.032311
15 C. P. Yang and S. Han, Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED, Phys. Rev. A 73(3), 032317 (2006)
https://doi.org/10.1103/PhysRevA.73.032317
16 W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, One-step implementation of multi-qubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Qsilica microsphere cavity, Appl. Phys. Lett. 96(24), 241113 (2010)
https://doi.org/10.1063/1.3455891
17 S. B. Zheng, Implementation of Toffoli gates with a single asymmetric Heisenberg XYinteraction, Phys. Rev. A 87(4), 042318 (2013)
https://doi.org/10.1103/PhysRevA.87.042318
18 T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett. 102(4), 040501 (2009)
https://doi.org/10.1103/PhysRevLett.102.040501
19 H. R. Wei and F. G. Deng, Universal quantum gates for hybrid systems assisted by quantum dots inside doublesided optical microcavities, Phys. Rev. A 87(2), 022305 (2013)
https://doi.org/10.1103/PhysRevA.87.022305
20 H. W. Wei and F. G. Deng, Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities,Sci. Rep. 4(1), 7551 (2014)
https://doi.org/10.1038/srep07551
21 M. Hua, M. J. Tao, and F. G. Deng, Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics, Phys. Rev. A 90(1), 012328 (2014)
https://doi.org/10.1103/PhysRevA.90.012328
22 M. Hua, M. J. Tao, and F. G. Deng, Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED, Sci. Rep. 5(1), 9274 (2015)
https://doi.org/10.1038/srep09274
23 C. P. Yang, Y. X. Liu, and F. Nori, Phase gate of one qubit simultaneously controlling n qubits in a cavity, Phys. Rev. A 81(6), 062323 (2010)
https://doi.org/10.1103/PhysRevA.81.062323
24 C. P. Yang, S. B. Zheng, and F. Nori, Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity, Phys. Rev. A 82(6), 062326 (2010)
https://doi.org/10.1103/PhysRevA.82.062326
25 C. P. Yang, Q. P. Su, F. Y. Zhang, and S. B. Zheng, Single-step implementation of a multiple-target-qubit controlled phase gate without need of classical pulses, Opt. Lett. 39(11), 3312 (2014)
https://doi.org/10.1364/OL.39.003312
26 H. F. Wang, A. D. Zhu, and S. Zhang, One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities, Opt. Lett. 39(6), 1489 (2014)
https://doi.org/10.1364/OL.39.001489
27 T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, Multi-target-qubit unconventional geometric phase gate in a multicavity system, Sci. Rep. 6(1), 21562 (2016)
https://doi.org/10.1038/srep21562
28 N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Extending the lifetime of a quantum bit with error correction in superconducting circuits, Nature 536(7617), 441 (2016)
https://doi.org/10.1038/nature18949
29 M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: a new paradigm for universal quantum computation, New J. Phys. 16(4), 045014 (2014)
https://doi.org/10.1088/1367-2630/16/4/045014
30 S. E. Nigg, Deterministic hadamard gate for microwave cat-state qubits in circuit QED, Phys. Rev. A 89(2), 022340 (2014)
https://doi.org/10.1103/PhysRevA.89.022340
31 C. P. Yang, Q. P. Su, S. B. Zheng, F. Nori, and S. Han, Entangling two oscillators with arbitrary asymmetric initial states, Phys. Rev. A 95(5), 052341 (2017)
https://doi.org/10.1103/PhysRevA.95.052341
32 R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a universal gate set on a logical qubit encoded in an oscillator, arXiv: 1608.02430 (2016)
33 C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, A Schrödinger cat living in two boxes, Science 352(6289), 1087 (2016)
https://doi.org/10.1126/science.aaf2941
34 C. P. Yang, S. I. Chu, and S. Han, Possible realization of entanglement, logical gates, and quantuminformation transfer with superconducting-quantuminterference-device qubits in cavity QED, Phys. Rev. A 67(4), 042311 (2003)
https://doi.org/10.1103/PhysRevA.67.042311
35 J. Q. You and F. Nori, Quantum information processing with superconducting qubits in a microwave field,Phys. Rev. B 68(6), 064509 (2003)
https://doi.org/10.1103/PhysRevB.68.064509
36 A. Blais, R. S. Huang, A. Wallra, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69(6), 062320 (2004)
https://doi.org/10.1103/PhysRevA.69.062320
37 J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58(11), 42 (2005)
https://doi.org/10.1063/1.2155757
38 J. Clarke and F. K. Wilhelm, Superconducting quantum bits, Nature 453(7198), 1031 (2008)
https://doi.org/10.1038/nature07128
39 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
40 Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85(2), 623 (2013)
https://doi.org/10.1103/RevModPhys.85.623
41 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
42 M. AbuGhanem, A. H. Homid, and M. Abdel-Aty, Cavity control as a new quantum algorithms implementation treatment, Front. Phys. 13, 130303 (2018)
https://doi.org/10.1007/s11467-017-0709-3
43 H. P. Cui, Y. Shan, J. Zou, and B. Shao, Entanglement reciprocation between two charge qubits and cavity field, Front. Phys. China 3, 258 (2008)
https://doi.org/10.1007/s11467-008-0030-2
44 P. B. Li, Y. C. Liu, S. Y. Gao, Z. L. Xiang, P. Rabl, Y. F. Xiao, and F. L. Li, Hybrid quantum device based on NV centers in diamond nanomechanical resonators plus superconducting waveguide cavities,Phys. Rev. Applied 4, 044003 (2015)
https://doi.org/10.1103/PhysRevApplied.4.044003
45 P. B. Li, S. Y. Gao, and F. L. Li, Engineering two-mode entangled states between two superconducting resonators by dissipation, Phys. Rev. A 86, 012318 (2012)
https://doi.org/10.1103/PhysRevA.86.012318
46 M. Šašura and V. Buzek, Multiparticle entanglement with quantum logic networks: Application to cold trapped ions, Phys. Rev. A 64(1), 012305 (2001)
https://doi.org/10.1103/PhysRevA.64.012305
47 F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing, CRC Press, USA, 2008
https://doi.org/10.1201/b15868
48 T. Beth and M. Rötteler, Quantum Information, Springer, Berlin, 2001, Vol. 173, Ch. 4, p. 96
https://doi.org/10.1007/3-540-44678-8_4
49 S. L. Braunstein, V. Buzek, and M. Hillery, Quantuminformation distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit, Phys. Rev. A 63(5), 052313 (2001)
https://doi.org/10.1103/PhysRevA.63.052313
50 J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76(4), 042319 (2007)
https://doi.org/10.1103/PhysRevA.76.042319
51 D. Sank, Z. Chen, M. Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, A. Vainsencher, T. White, J. Wenner, A. N. Korotkov, and J. M. Martinis, Measurement-induced state transitions in a superconducting qubit: beyond the rotating wave approximation, Phys. Rev. Lett. 117(19), 190503 (2016)
https://doi.org/10.1103/PhysRevLett.117.190503
52 P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, Using sideband transitions for two-qubit operations in superconducting circuits, Phys. Rev. B 79(18), 180511 (2009)
https://doi.org/10.1103/PhysRevB.79.180511
53 R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O’Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and J. M. Martinis, Coherent Josephson qubit suitable for scalable quantum integrated circuits, Phys. Rev. Lett. 111(8), 080502 (2013)
https://doi.org/10.1103/PhysRevLett.111.080502
54 M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, and J. M. Martinis, Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state, Nat. Phys. 4(7), 523 (2008)
55 M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Tuning the field in a microwave resonator faster than the photon lifetime, Appl. Phys. Lett. 92(20), 203501 (2008)
https://doi.org/10.1063/1.2929367
56 Z. L. Wang, Y. P. Zhong, L. J. He, H. Wang, J. M. Martinis, A. N. Cleland, and Q. W. Xie, Quantum state characterization of a fast tunable superconducting resonator, Appl. Phys. Lett. 102(16), 163503 (2013)
https://doi.org/10.1063/1.4802893
57 D. F. James and J. Jerke, Effective hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)
https://doi.org/10.1139/p07-060
58 Q. P. Su, H. H. Zhu, L. Yu, Y. Zhang, S. J. Xiong, J. M. Liu, and C. P. Yang, Generating double NOON states of photons in circuit QED, Phys. Rev. A 95(2), 022339 (2017)
https://doi.org/10.1103/PhysRevA.95.022339
59 C. P. Yang, Q. P. Su, S. B. Zheng, and S. Han, One-step transfer or exchange of arbitrary multipartite quantum states with a single-qubit coupler, Phys. Rev. B 92(5), 054509 (2015)
https://doi.org/10.1103/PhysRevB.92.054509
60 Y. X. Liu, S. K. Özdemir, A. Miranowicz, and N. Imoto, Kraus representation of a damped harmonic oscillator and its application, Phys. Rev. A 70, 042308 (2004)
https://doi.org/10.1103/PhysRevA.70.042308
61 C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, Crosstalkinsensitive method for simultaneously coupling multiple pairs of resonators, Phys. Rev. A 93(4), 042307 (2016)
https://doi.org/10.1103/PhysRevA.93.042307
62 J. A. Schreier, A. A. Houck, J. Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Suppressing charge noise decoherence in superconducting charge qubits, Phys. Rev. B 77, 180502(R) (2008)
63 T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys. 6(10), 772 (2010)
64 For a transmon qutrit, the |g〉↔|f〉 transition is much weaker than those of the |g〉↔|e〉 and |e〉↔|g〉 transitions. Thus, we have γ–1eg, γ–1fg.
65 C. Rigetti, S. Poletto, J. M. Gambetta, B. L. T. Plourde, J. M. Chow, et al., Superconducting qubit in waveguide cavity with coherence time approaching 0.1 ms, Phys. Rev. B 86, 100506(R) (2012)
66 M. J. Peterer, S. J. Bader, X. Jin, F. Yan, A. Kamal, T. J. Gudmundsen, P. J. Leek, T. P. Orlando, W. D. Oliver, and S. Gustavsson, Coherence and decay of higher energy levels of a superconducting transmon qubit, Phys. Rev. Lett. 114, 010501 (2015)
https://doi.org/10.1103/PhysRevLett.114.010501
67 A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481, 170 (2011)
https://doi.org/10.1038/nature10713
68 M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, A quantum memory with near-millisecond coherence in circuit QED, Phys. Rev. B 94(1), 014506 (2016)
https://doi.org/10.1103/PhysRevB.94.014506
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed