Nearly deterministic controlled-not gate with weak cross-kerr nonlinearities

On the basis of the probe coherent state and weak cross-Kerr nonlinearities, we present a scheme of a nearly deterministic Controlled-NOT gate. In this construction, feed-forward methods, quantum nondemolition detectors and several optical elements are applied. It is a potentially practical quantum gate with certain features. First, the lack of auxiliary photons is allowable, which decreases consumption of resources. Secondly, employment of the signal photon from either of target output ports and three quantum nondemolition detectors enable the success probability to approach unit and judge whether the signal photons lose or not. Thirdly, the displacement measurement is adopted, and thus the Controlled-NOT gate works against photon loss of the probe coherent state. Finally, in order to circumvent the effect of dephasing, the monochromatic signal photons are exploited.

[1]  Masato Koashi,et al.  Probabilistic manipulation of entangled photons , 2001 .

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

[3]  T. Spiller,et al.  Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening , 2009, 0902.2252.

[4]  M. J. Fitch,et al.  Experimental controlled-NOT logic gate for single photons in the coincidence basis , 2003, quant-ph/0303095.

[5]  D. Leibfried,et al.  Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate , 2003, Nature.

[6]  Ran Li,et al.  High-fidelity universal quantum gates through group-symmetrized rapid passage , 2010, 1004.0710.

[7]  Chuang,et al.  Quantum bit regeneration. , 1996, Physical review letters.

[8]  Kae Nemoto,et al.  Loss in hybrid qubit-bus couplings and gates , 2008, 0804.3240.

[9]  John C. Howell,et al.  Nondestructive single-photon trigger , 2000 .

[10]  T. Spiller,et al.  Quantum computation by communication , 2005, quant-ph/0509202.

[11]  F. Khalili,et al.  Quantum nondemolition measurements: the route from toys to tools , 1996 .

[12]  Julio Gea-Banacloche,et al.  Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets , 2009, 0911.4682.

[13]  F. Schmidt-Kaler,et al.  Realization of the Cirac–Zoller controlled-NOT quantum gate , 2003, Nature.

[14]  Phoenix,et al.  Wave-packet evolution in the damped oscillator. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[15]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[16]  W. Munro,et al.  A near deterministic linear optical CNOT gate , 2004 .

[17]  Pieter Kok,et al.  Effects of self-phase-modulation on weak nonlinear optical quantum gates , 2007, 0710.1810.

[18]  Jian Li,et al.  Quantum control gates with weak cross-Kerr nonlinearity , 2008, 0811.3364.

[19]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[20]  E. Knill.  Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics , 2003, quant-ph/0307015.

[21]  Jeffrey H. Shapiro,et al.  Continuous-time cross-phase modulation and quantum computation , 2007 .

[22]  Gerard J. Milburn,et al.  State reduction in quantum-counting quantum nondemolition measurements , 1984 .

[23]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[24]  Kae Nemoto,et al.  The efficiencies of generating cluster states with weak nonlinearities , 2006, quant-ph/0607060.

[25]  K. Mølmer,et al.  QUANTUM COMPUTATION WITH IONS IN THERMAL MOTION , 1998, quant-ph/9810039.

[26]  Gilles Nogues,et al.  Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED , 1999 .

[27]  C. Gerry,et al.  Quantum non-demolition measurement of photon number using weak nonlinearities , 2008 .

[28]  Kae Nemoto,et al.  Weak nonlinearities and cluster states , 2007, 0704.1931.

[29]  Ran Li,et al.  High-fidelity universal quantum gates , 2010, Quantum Inf. Comput..

[30]  Anton Zeilinger,et al.  General properties of lossless beam splitters in interferometry , 1981 .

[31]  Qi Guo,et al.  Simplified optical quantum-information processing via weak cross-Kerr nonlinearities , 2011 .

[32]  T. Spiller,et al.  Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities , 2004, quant-ph/0408117.

[33]  Jie Song,et al.  Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity , 2011 .

[34]  G. J. Milburn,et al.  Quantum-information processing via a lossy bus , 2006, quant-ph/0607206.

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

[36]  Jeffrey H. Shapiro,et al.  Single-photon Kerr nonlinearities do not help quantum computation , 2006 .

[37]  Stephen A. Fenner,et al.  Efficient universal quantum circuits , 2009, Quantum Inf. Comput..

[38]  Yan Xia,et al.  Controlled implementation of two-photon controlled phase gate within a network , 2010, Quantum Inf. Comput..

[39]  J. D. Franson,et al.  Probabilistic quantum logic operations using polarizing beam splitters , 2001, quant-ph/0107091.

[40]  Yamamoto,et al.  Quantum nondemolition measurement of the photon number via the optical Kerr effect. , 1985, Physical review. A, General physics.

[41]  Vittorio Degiorgio,et al.  Phase shift between the transmitted and the reflected optical fields of a semireflecting lossless mirror is π/2 , 1980 .

[42]  Yong Zhang,et al.  Polarization-entanglement purification and concentration using cross-kerr nonlinearity , 2011, Quantum Inf. Comput..

[43]  Hyunseok Jeong.  Quantum computation using weak nonlinearities: Robustness against decoherence , 2006 .

[44]  Kae Nemoto,et al.  Weak nonlinearities: a new route to optical quantum computation , 2005, quant-ph/0507084.