Shortcuts to adiabatic for implementing controlled phase gate with Cooper-pair box qubits in circuit quantum electrodynamics system

We theoretically present a protocol to realize the controlled phase gate with Cooper-pair box (CPB) qubits in circuit quantum electrodynamics (circuit QED) system. In this protocol, the one-dimensional transmission line resonator in circuit QED system acting as quantum data bus generates a common cavity mode and interacts with each CPB qubit. The Rabi frequencies of driven pluses can be designed with simple Gaussian or trigonometric functions by utilizing the universal SU(2) transformation. Moreover, the level configurations of CPB qubits have been reported by previous protocol (Feng and Zhang in Phys C 470:240–243, 2010). Thus, the protocol can be realized easily in experiment. In addition, the influence of various decoherence processes such as spontaneous emissions, dephasings of the CPB qubits and the decay of the cavity mode on the fidelity is discussed by numerical simulations. The results show that the protocol is robust against the decoherence and parameter variations. Therefore, the protocol may be useful for the fields of quantum computations.

[1]  DiVincenzo.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[2]  Jing-Ji Wen,et al.  One-step implementation of the Rydberg-Rydberg-interaction gate , 2016 .

[3]  Y. Ng.  From computation to black holes and space-time foam. , 2000, Physical review letters.

[4]  Patrizia Vignolo,et al.  Shortcut to adiabaticity for an interacting Bose-Einstein condensate , 2010, 1009.5868.

[5]  H. J. Kimble,et al.  Robust quantum gates on neutral atoms with cavity-assisted photon scattering , 2005 .

[6]  Yan Xia,et al.  Two-photon phase gate with linear optical elements and atom–cavity system , 2016, Quantum Inf. Process..

[7]  Qing Ai,et al.  Erratum: Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics [Phys. Rev. A93, 052324 (2016)] , 2016 .

[8]  M. Berry,et al.  Transitionless quantum driving , 2009 .

[9]  Shou Zhang,et al.  Dressed-state scheme for a fast CNOT gate , 2016, Quantum Inf. Process..

[10]  Mang Feng,et al.  Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference , 2007 .

[11]  A. Baksic,et al.  Supplementary information for “ Speeding up adiabatic quantum state transfer by using dressed states ” , 2016 .

[12]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  Shou Zhang,et al.  Fast Rydberg antiblockade regime and its applications in quantum logic gates , 2017 .

[14]  J. G. Muga,et al.  Shortcut to adiabatic passage in two- and three-level atoms. , 2010, Physical review letters.

[15]  Qi‐Cheng Wu,et al.  Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms , 2016, 1604.06301.

[16]  Lituo Shen,et al.  Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity , 2013, 1310.5323.

[17]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[18]  Yang Han,et al.  Fast quantum phase gate in a small-detuning circuit QED model , 2010 .

[19]  Fast quantum state engineering via universal SU(2) transformation , 2017, 1708.03433.

[20]  Chui-Ping Yang,et al.  Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED , 2003, 1403.4037.

[21]  Xi Chen,et al.  Improving shortcuts to adiabaticity by iterative interaction pictures , 2013 .

[22]  Qi‐Cheng Wu,et al.  Improving the stimulated Raman adiabatic passage via dissipative quantum dynamics. , 2016, Optics express.

[23]  Shi-Biao Zheng,et al.  Quantum logic gates for two atoms with a single resonant interaction , 2005 .

[24]  Yan Xia,et al.  Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems , 2014, 1401.4291.

[25]  E. Torrontegui,et al.  Shortcuts to adiabaticity for non-Hermitian systems , 2011, 1106.2776.

[26]  J. G. Muga,et al.  Engineering of fast population transfer in three-level systems , 2012 .

[27]  E. Torrontegui,et al.  Lewis-Riesenfeld invariants and transitionless quantum driving , 2011, 1102.3449.

[28]  F. Nori,et al.  Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems , 2012, 1204.2137.

[29]  Qing Ai,et al.  Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics , 2016, 1602.00050.

[30]  Xue-ke Song,et al.  Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm , 2015, 1509.00097.

[31]  Xiao-Qiang Shao,et al.  Efficient scheme for implementing an N -qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics , 2007 .

[32]  N. Vitanov.  Synthesis of arbitrary SU(3) transformations of atomic qutrits , 2012 .

[33]  T. R. Tan,et al.  Coherent diabatic ion transport and separation in a multizone trap array. , 2012, Physical review letters.

[34]  Jingwei Chen,et al.  Deterministic implementations of quantum gates with circuit QEDs via Stark-chirped rapid adiabatic passages , 2015 .

[35]  J. G. Muga,et al.  Frictionless dynamics of Bose–Einstein condensates under fast trap variations , 2009, 0910.2992.

[36]  Yu Zhang,et al.  Universal controlled-phase gate with cat-state qubits in circuit QED , 2017, 1706.07083.

[37]  Wojciech H Zurek,et al.  Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model. , 2012, Physical review letters.

[38]  Franco Nori,et al.  Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit. , 2005, Physical review letters.

[39]  Sleator,et al.  Realizable Universal Quantum Logic Gates. , 1995, Physical review letters.

[40]  Jiangfeng Du,et al.  Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system. , 2012, Physical review letters.

[41]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[42]  A. Campo,et al.  Shortcuts to adiabaticity by counterdiabatic driving. , 2013, Physical review letters.

[43]  Stuart A. Rice,et al.  Adiabatic Population Transfer with Control Fields , 2003 .

[44]  S. Lloyd.  Ultimate physical limits to computation , 1999, Nature.

[45]  Stuart A Rice,et al.  On the consistency, extremal, and global properties of counterdiabatic fields. , 2008, The Journal of chemical physics.

[46]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[47]  D. Alonso,et al.  Optimally robust shortcuts to population inversion in two-level quantum systems , 2012, 1206.1691.

[48]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[49]  E Solano,et al.  Ultrafast quantum gates in circuit QED. , 2011, Physical review letters.

[50]  E Torrontegui,et al.  Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity. , 2011, Physical review letters.

[51]  J. G. Muga,et al.  Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. , 2009, Physical review letters.

[52]  Lov K. Grover.  Quantum Computers Can Search Rapidly by Using Almost Any Transformation , 1998 .

[53]  Klaus Molmer,et al.  Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems , 2007 .

[54]  Shi Hu,et al.  Scheme for implementing multitarget qubit controlled-NOT gate of photons and controlled-phase gate of electron spins via quantum dot-microcavity coupled system , 2016, Quantum Inf. Process..

[55]  Alexandre Blais,et al.  Quantum information processing with circuit quantum electrodynamics , 2007 .

[56]  Shuo-Yen Tseng,et al.  Engineering of fast mode conversion in multimode waveguides. , 2012, Optics letters.

[57]  Yan Xia,et al.  Shortcuts to adiabatic for implementing controlled-not gate with superconducting quantum interference device qubits , 2018, Quantum Inf. Process..

[58]  Zhi‐Bo Feng,et al.  Scalable geometric quantum computing with Cooper-pair box qubits in circuit QED , 2010 .

[59]  Yan Xia,et al.  Fast preparation of W states with superconducting quantum interference devices by using dressed states , 2016, 1610.07751.

[60]  Patrizia Vignolo,et al.  Fast optimal transition between two equilibrium states , 2010, 1006.1495.

[61]  Yan Xia,et al.  Shortcuts to adiabatic passage for multiparticles in distant cavities: applications to fast and noise-resistant quantum population transfer, entangled states’ preparation and transition , 2014, 1405.7779.

[62]  Hui Yan,et al.  Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers , 2016, 1604.07914.

[63]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[64]  P. Joyez,et al.  Manipulating the Quantum State of an Electrical Circuit , 2002, Science.

[65]  A Walther,et al.  Controlling fast transport of cold trapped ions. , 2012, Physical review letters.

[66]  Shi-Biao Zheng.  Unconventional geometric quantum phase gates with a cavity QED system (4 pages) , 2004 .

[67]  Barenco,et al.  Conditional Quantum Dynamics and Logic Gates. , 1995, Physical review letters.

[68]  J. G. Muga,et al.  Interferometer with a driven trapped ion , 2018, Physical Review A.

[69]  S. Danilin,et al.  Stimulated Raman adiabatic passage in a three-level superconducting circuit , 2015, Nature Communications.

[70]  A. del Campo,et al.  Frictionless quantum quenches in ultracold gases: A quantum-dynamical microscope , 2011, 1103.0714.

[71]  Yan Xia,et al.  Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states , 2014, 1410.8285.

[72]  Bao-Jie Liu,et al.  Superadiabatic Holonomic Quantum Computation in Cavity QED , 2016, 1610.03661.

[73]  X Wang,et al.  Multibit gates for quantum computing. , 2001, Physical review letters.

[74]  Siyuan Han,et al.  Realization of an n -qubit controlled- U gate with superconducting quantum interference devices or atoms in cavity QED , 2006 .

[75]  J. G. Muga,et al.  Shortcuts to Adiabaticity , 2012, 1212.6343.

[76]  Liang,et al.  Time-dependent quantum systems and the invariant Hermitian operator. , 1996, Physical review. A, Atomic, molecular, and optical physics.