## Physical optimization of quantum error correction circuits with spatially separated quantum dot spins |

Optics Express, Vol. 21, Issue 10, pp. 12484-12494 (2013)

http://dx.doi.org/10.1364/OE.21.012484

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### Abstract

We propose an efficient protocol for optimizing the physical implementation of three-qubit quantum error correction with spatially separated quantum dot spins via virtual-photon-induced process. In the protocol, each quantum dot is trapped in an individual cavity and each two cavities are connected by an optical fiber. We propose the optimal quantum circuits and describe the physical implementation for correcting both the bit flip and phase flip errors by applying a series of one-bit unitary rotation gates and two-bit quantum iSWAP gates that are produced by the long-range interaction between two distributed quantum dot spins mediated by the vacuum fields of the fiber and cavity. The protocol opens promising perspectives for long distance quantum communication and distributed quantum computation networks.

© 2013 OSA

**OCIS Codes**

(270.5580) Quantum optics : Quantum electrodynamics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: March 4, 2013

Revised Manuscript: April 23, 2013

Manuscript Accepted: April 23, 2013

Published: May 14, 2013

**Citation**

Hong-Fu Wang, Ai-Dong Zhu, and Shou Zhang, "Physical optimization of quantum error correction circuits with spatially separated quantum dot spins," Opt. Express **21**, 12484-12494 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12484

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### References

- P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science, Los Alamitos, California(IEEE Computer Society, 1994), pp. 124–134
- L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett.79, 325–328 (1997). [CrossRef]
- M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, “Tight Bounds on Quantum Searching,” Fortschr. Phys.46, 493–505 (1998). [CrossRef]
- A. Y. Kitaev, “Quantum measurements and the Abelian Stabilizer Problem,” quant-ph/9511026 .
- D. Simon, “On the power of quantum computation,” inProceedings of the Symposium on the Foundations of Computer Science, Los Alamitos, California (IEEE Computer Society, 1994) , pp. 116–123
- R. Jozsa, “Quantum Algorithms and the Fourier Transform,” quant-ph/9707033 .
- C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993). [CrossRef] [PubMed]
- C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992). [CrossRef] [PubMed]
- C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68, 3121–3124 (1992). [CrossRef] [PubMed]
- F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A68, 042317 (2003). [CrossRef]
- F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A68, 042315 (2003). [CrossRef]
- F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A69, 052319 (2004) [CrossRef]
- P. W. Shor, “Fault-tolerant quantum computation,” in Proceedings of the 37th Symposium on Foundations of Computing(IEEE Computer Society, 1996), pp. 56–65; e-print quant-ph/9605011 .
- D. P. DiVincenzo and P. W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes,” Phys. Rev. Lett.77, 3260–3263 (1996). [CrossRef] [PubMed]
- M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information” (Cambridge University, 2000).
- H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express19, 25433–25440 (2011) [CrossRef]
- P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A52, 2493(R)–2496(R) (1995). [CrossRef]
- R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect Quantum Error Correcting Code,” Phys. Rev. Lett.77, 198–201 (1996). [CrossRef] [PubMed]
- C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A54, 3824–3851 (1996). [CrossRef] [PubMed]
- A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett.77, 793–797 (1996). [CrossRef] [PubMed]
- E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Phys. Rev. A55, 900–911 (1997). [CrossRef]
- D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett.81, 2152–2155 (1998). [CrossRef]
- G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999). [CrossRef]
- O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011). [CrossRef] [PubMed]
- J. W. Pan, C Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature410, 1067–1070 (2001). [CrossRef] [PubMed]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A77, 042308 (2008). [CrossRef]
- Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A81, 032307 (2010). [CrossRef]
- F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (2011). [CrossRef]
- H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled three-photon W states,” Eur. Phys. J. D56, 271–275 (2010). [CrossRef]
- H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled three-photon W states,” J. Opt. Soc. Am. B27, 2159–2164 (2010). [CrossRef]
- H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown atomic entangled states by interference of polarized photons,” J. Phys. B: At. Mol. Opt. Phys.43, 235501 (2010). [CrossRef]
- C. Wang, Y. Zhao, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A84, 032307 (2011). [CrossRef]
- Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A85, 012307 (2012). [CrossRef]
- Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A85, 042302 (2012). [CrossRef]
- Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quantum. Inf. Process.12, 1885–1895 (2013). [CrossRef]
- Y. B. Sheng and L. Zhou, “Efficient W-state entanglement concentration using quantum-dot and optical micro-cavities,” J. Opt. Soc. Am. B30, 678–686 (2013). [CrossRef]
- D. Stepanenko and G. Burkard, “Quantum gates between capacitively coupled double quantum dot two-spin qubits,” Phys. Rev. B75, 085324 (2007). [CrossRef]
- J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, “Relaxation, dephasing, and quantum control of electron spins in double quantum dots,” Phys. Rev. B76, 035315 (2007). [CrossRef]
- K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009). [CrossRef] [PubMed]
- G. Shinkai, T. Hayashi, T. Ota, and T. Fujisawa, “Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 056802 (2009). [CrossRef] [PubMed]
- T. Meunier, V. E. Calado, and L. M. K. Vandersypen, “Efficient controlled-phase gate for single-spin qubits in quantum dots,” Phys. Rev. B83, 121403(R)(2011). [CrossRef]
- R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys.79, 1217–1265 (2007). [CrossRef]
- D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A57, 120–126 (1998) [CrossRef]
- A. Imamoḡlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum Information Processing Using Quantum Dot Spins and Cavity QED,” Phys. Rev. Lett.83, 4204–4207 (1999). [CrossRef]
- C. Y. Hsieh and P. Hawrylak, “Quantum circuits based on coded qubits encoded in chirality of electron spin complexes in triple quantum dots,” Phys. Rev. B82, 205311 (2010). [CrossRef]
- C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B83, 115303 (2011). [CrossRef]
- A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, “Phonon mediated off-resonant quantum dot-cavity coupling under resonant excitation of the quantum dot,” Phys. Rev. B84, 085309 (2011). [CrossRef]
- A. Serafini, S. Mancini, and S. Bose, “Distributed Quantum Computation via Optical Fibers,” Phys. Rev. Lett.96, 010503 (2006). [CrossRef] [PubMed]
- H. F. Wang, S. Zhang, A. D. Zhu, and K. H. Yeon, “Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities,” J. Opt. Soc. Am. B29, 1078–1084 (2012). [CrossRef]
- S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett.94, 154101 (2009). [CrossRef]
- S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B19, 064204 (2010). [CrossRef]
- N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A67, 032301 (2003). [CrossRef]
- G. Burkard, D. Loss, and D. P. DiVincenzo, “Coupled quantum dots as quantum gates,” Phys. Rev. B59, 2070–2078 (1999). [CrossRef]
- D. P. DiVincenzo, “Quantum computing and single-qubit measurements using the spin-filter effect,” J. Appl. Phys.85, 4785–4787 (1999). [CrossRef]
- B. Schumacher, “Sending entanglement through noisy quantum channels,” Phys. Rev. A54, 2614–2628 (1996). [CrossRef] [PubMed]

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