Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity

To date, all work concerning the construction of quantum logic gates, an essential part of quantum computing, has focused on operating in one degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of achieving scalable photonic quantum computing based on two DOFs for quantum systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating in both the spatial mode and polarization DOFs for a photon pair simultaneously, using the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a one-side optical microcavity as a result of cavity quantum electrodynamics. With this hyper-CNOT gate and linear optical elements, two-photon four-qubit cluster entangled states can be prepared and analyzed, which give an application to manipulate more information with less resources. We analyze the experimental feasibility of this hyper-CNOT gate and show that it can be implemented with current technology.

[1]  Gilberto Medeiros-Ribeiro,et al.  Charged Excitons in Self-Assembled Semiconductor Quantum Dots , 1997 .

[2]  P. Knight,et al.  Proposal for teleportation of an atomic state via cavity decay , 1999, quant-ph/9908004.

[3]  Fuguo Deng,et al.  Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement , 2010 .

[4]  Fuguo Deng,et al.  One-step deterministic polarization-entanglement purification using spatial entanglement , 2010, 1008.3509.

[5]  Guilu Long,et al.  Experimental realization of nonadiabatic holonomic quantum computation. , 2013, Physical review letters.

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

[7]  Jian-Wei Pan,et al.  Realization of a photonic controlled-NOT gate sufficient for quantum computation. , 2004, Physical Review Letters.

[8]  J. P. Woerdman,et al.  Experimental demonstration of fractional orbital angular momentum entanglement of two photons. , 2005, Physical review letters.

[9]  Pierre M. Petroff,et al.  A Coherent Single-Hole Spin in a Semiconductor , 2009, Science.

[10]  J. L. O'Brien,et al.  Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon , 2007, 0708.2019.

[11]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[12]  Guang-Can Guo,et al.  Methods for a linear optical quantum Fredkin gate , 2008, 0804.0992.

[13]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

[14]  G. Rupper,et al.  Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity , 2004, Nature.

[15]  Cristian Bonato,et al.  CNOT and Bell-state analysis in the weak-coupling cavity QED regime. , 2010, Physical review letters.

[16]  Debbie W. Leung,et al.  Realization of quantum process tomography in NMR , 2000, quant-ph/0012032.

[17]  H. Weinfurter,et al.  Linear optics controlled-phase gate made simple. , 2005, Physical Review Letters.

[18]  A. Zeilinger,et al.  Experimental one-way quantum computing , 2005, Nature.

[19]  W. Munro,et al.  Quantum error correction for beginners , 2009, Reports on progress in physics. Physical Society.

[20]  Yu-Bo Sheng,et al.  Complete hyperentangled-Bell-state analysis for quantum communication , 2010, 1103.0230.

[21]  Harald Weinfurter,et al.  Embedded Bell-state analysis , 1998 .

[22]  Fuguo Deng,et al.  Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity , 2008, 0805.0032.

[23]  C. Beenakker,et al.  Charge detection enables free-electron quantum computation. , 2004, Physical Review Letters.

[24]  T. Ralph,et al.  Demonstration of an all-optical quantum controlled-NOT gate , 2003, Nature.

[25]  V. Kulakovskii,et al.  Strong coupling in a single quantum dot–semiconductor microcavity system , 2004, Nature.

[26]  Jacob M. Taylor,et al.  Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots , 2005, Science.

[27]  Keiji Sasaki,et al.  Demonstration of an optical quantum controlled-NOT gate without path interference. , 2005, Physical review letters.

[28]  Jaromir Fiurasek.  Linear-optics quantum Toffoli and Fredkin gates , 2006 .

[29]  W. J. Munro,et al.  Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity , 2009, 0910.4549.

[30]  William J. Munro,et al.  Deterministic photon entangler using a charged quantum dot inside a microcavity , 2008 .

[31]  C. Hu,et al.  Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity , 2010, 1005.5545.

[32]  Dirk Reuter,et al.  Radiatively limited dephasing in InAs quantum dots , 2004 .

[33]  Christian Schneider,et al.  Quantum dot induced phase shift in a pillar microcavity , 2011 .

[34]  Jian-Wei Pan,et al.  Polarization entanglement purification using spatial entanglement. , 2001, Physical review letters.

[35]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

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

[37]  Christian Kurtsiefer,et al.  Complete deterministic linear optics Bell state analysis. , 2006, Physical review letters.

[38]  D. R. Yakovlev,et al.  Optically detected magnetic resonance of excess electrons in type-I quantum wells with a low-density electron gas , 1998 .

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

[40]  Jaromir Fiurasek,et al.  Linear optical Fredkin gate based on partial-SWAP gate , 2008, 0809.3228.