Warning: Invalid argument supplied for foreach() in /home/www/wordpress/wp-content/plugins/o3po/includes/class-o3po-crossref.php on line 189
Quantum gates between distant qubits via spin-independent scattering
1Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT, UK
2QOLS, Blackett Laboratory, Imperial College London, SW7 2AZ, UK
3C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, NY 11794-3840, USA
Published: | 2017-11-30, volume 1, page 36 |
Eprint: | arXiv:1412.3582v4 |
Doi: | https://doi.org/10.22331/q-2017-11-30-36 |
Citation: | Quantum 1, 36 (2017). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We show how the spin independent scattering of two initially distant qubits, say, in distinct traps or in remote sites of a lattice, can be used to implement an entangling quantum gate between them. The scattering takes place under 1D confinement for which we consider two different scenarios: a 1D wave-guide and a tight-binding lattice. We consider models with contact-like interaction between two fermionic or two bosonic particles. A qubit is encoded in two distinct spins (or other internal) states of each particle. Our scheme enables the implementation of a gate between two qubits which are initially too far to interact directly, and provides an alternative to photonic mediators for the scaling of quantum computers. Fundamentally, an interesting feature is that "identical particles" (e.g., two atoms of the same species) and the 1D confinement, are both necessary for the action of the gate. Finally, we discuss the feasibility of our scheme, the degree of control required to initialize the wave-packets momenta, and show how the quality of the gate is affected by momentum distributions and initial distance. In a lattice, the control of quasi-momenta is naturally provided by few local edge impurities in the lattice potential.
![](https://quantum-journal.org/wp-content/uploads/2017/11/scattering2.jpg)
► BibTeX data
► References
[1] C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, A. Kuhn, New. J. Phys 14, 073051 (2012).
https://doi.org/10.1088/1367-2630/14/7/073051
[2] M. Schlosser, J. Kruse, C. Gierl, S. Teichmann, S. Tichelmann, G. Birkl, New. J. Phys. 14, 123034 (2012).
https://doi.org/10.1088/1367-2630/14/12/123034
[3] D. Barredo et al., Phys. Rev. Lett. 114, 113002 (2015).
https://doi.org/10.1103/PhysRevLett.114.113002
[4] M. Saffman, J. Phys. B: At. Mol. Opt. Phys. 49 202001 (2016).
https://doi.org/10.1088/0953-4075/49/20/202001
[5] T. Fukuhara et al., Nature 502, 76-79 (2013).
https://doi.org/10.1038/nature12541
[6] P.M. Preiss, R. Ma, M.E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, M. Greiner, Science 347, 1229 (2015).
https://doi.org/10.1126/science.1260364
[7] D. Greif et al., Science 351, 953 (2016).
https://doi.org/10.1126/science.aad9041
[8] R. Bücker, J. Grond, S. Manz, T. Berrada, T. Betz, C. Koller, U. Hohenester, T. Schumm, A. Perrin, J. Schmiedmayer, Nature Physics 7, 608-611 (2011).
https://doi.org/10.1038/nphys1992
[9] E. Knill, R. Laflamme and G. Milburn, Nature 409, 46 (2001).
https://doi.org/10.1038/35051009
[10] C. W. J. Beenakker, D. P. DiVincenzo, C. Emary, and M. Kindermann, Phys. Rev. Lett. 93, 020501 (2004).
https://doi.org/10.1103/PhysRevLett.93.020501
[11] S. Popescu, Phys. Rev. Lett. 99, 250501 (2007).
https://doi.org/10.1103/PhysRevLett.99.250501
[12] L. -M. Duan and H. J. Kimble, Phys. Rev. Lett. 92, 127902 (2004).
https://doi.org/10.1103/PhysRevLett.92.127902
[13] D. G. Angelakis, M. F. Santos, V. Yannopapas and A. Ekert, Phys. Lett. A. 362, 377 (2007).
https://doi.org/10.1016/j.physleta.2006.10.046
[14] K. Nemoto and W. J. Munro, Phys. Rev. Lett 93, 250502 (2004).
https://doi.org/10.1103/PhysRevLett.93.250502
[15] A. Reiserer, N. Kalb, G. Rempe, S. Ritter, Nature 508, 237-240 (2014).
https://doi.org/10.1038/nature13177
[16] A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, M. D. Lukin, Phys. Rev. Lett. 105, 060502 (2010).
https://doi.org/10.1103/PhysRevLett.105.060502
[17] S. Bose and D. Home, Phys. Rev. Lett. 88, 050401 (2002).
https://doi.org/10.1103/PhysRevLett.88.050401
[18] F. Ciccarello et al., New J. of Phys. 8, 214 (2006); F. Ciccarello et al., Phys. Rev. Lett. 100, 150501 (2008).
https://doi.org/10.1103/PhysRevLett.100.150501
[19] L. Lamata and J. Leon, Phys. Rev. A 73, 052322 (2006).
https://doi.org/10.1103/PhysRevA.73.052322
[20] D. S. Saraga, B. L. Altshuler, D. Loss, and R. M. Westervelt, Phys. Rev. B 71, 045338 (2005).
https://doi.org/10.1103/PhysRevB.71.045338
[21] P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, Phys. Rev. B 70, 115330 (2004).
https://doi.org/10.1103/PhysRevB.70.115330
[22] G. Burkard, D. Loss, E. V. Sukhorukov, Phys. Rev. B 61, R16303(R) (2000).
https://doi.org/10.1103/PhysRevB.61.R16303
[23] G. Cordourier-Maruri et al., Phys. Rev. A 82, 052313 (2010).
https://doi.org/10.1103/PhysRevA.82.052313
[24] M. Lewenstein, B. A. Malomed, New J. Phys. 11, 113014 (2009).
https://doi.org/10.1088/1367-2630/11/11/113014
[25] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
https://doi.org/10.1103/PhysRevA.57.120
[26] D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000).
https://doi.org/10.1103/PhysRevLett.85.2208
[27] O. Mandel et al., Nature 425, 937 (2003).
https://doi.org/10.1038/nature02008
[28] R. Stock, I. H. Deutsch and E. L. Bolda, Phys. Rev. Lett. 91, 183201 (2003).
https://doi.org/10.1103/PhysRevLett.91.183201
[29] D. Hayes, P. S. Julienne and I. H. Deutsch, Phys. Rev. Lett. 98, 070501 (2007).
https://doi.org/10.1103/PhysRevLett.98.070501
[30] M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, J. V. Porto, Nature 448, 452 (2007).
https://doi.org/10.1038/nature06011
[31] L. Isenhower et al., Phys. Rev. Lett. 104, 010503 (2010).
https://doi.org/10.1103/PhysRevLett.104.010503
[32] T. Wilk et al., Phys. Rev. Lett. 104, 010502 (2010).
https://doi.org/10.1103/PhysRevLett.104.010502
[33] J. Hofmann et al., Science 337, 72 (2012).
https://doi.org/10.1126/science.1221856
[34] J.I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
https://doi.org/10.1103/PhysRevLett.74.4091
[35] T. P. Spiller et al., New J. Phys. 8, 30 (2006).
https://doi.org/10.1088/1367-2630/8/2/030
[36] L. Banchi, A. Bayat, P. Verrucchi, and S. Bose, Phys. Rev. Lett. 106, 140501 (2011).
https://doi.org/10.1103/PhysRevLett.106.140501
[37] X. Z. Zhang, Z. Song, Sci. Rep. 6, 18323 (2016).
https://doi.org/10.1038/srep18323
[38] V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, 1993; Eq.1.11, p 5.
[39] T. Kinoshita et al., Science 305, 1125 (2004).
https://doi.org/10.1126/science.1100700
[40] B. Paredes et al., Nature 429, 277 (2004). S. Hofferberth et al., Nature Phys. 4, 489 (2008).
https://doi.org/10.1038/nature02530
[41] A. H. van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008).
https://doi.org/10.1103/PhysRevLett.100.090402
[42] T. Betz et al., Phys. Rev. Lett. 106, 020407 (2011). \bibitem R. Bucker et al., Nature Physics 7, 608 (2011).
https://doi.org/10.1103/PhysRevLett.106.020407
[43] T. Calarco et al., Phys. Rev. A 61, 022304 (2000).
https://doi.org/10.1103/PhysRevA.61.022304
[44] D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W Gardiner, P. Zoller, Phys. Rev. Lett. 82, 1975 (1999).
https://doi.org/10.1103/PhysRevLett.82.1975
[45] E. T. Owen, M. C. Dean, and C. H. W. Barnes, Phys. Rev. A 85, 022319, (2012).
https://doi.org/10.1103/PhysRevA.85.022319
[46] W. Guerin et al., Phys. Rev. Lett. 97, 200402 (2006).
https://doi.org/10.1103/PhysRevLett.97.200402
[47] P. Wicke, S. Whitlock, and N. J. van Druten, arXiv:1010.4545v1 (2010).
arXiv:1010.4545v1
[48] M. J. Davis, P. B. Blakie, A. H. van Amerongen, N. J. van Druten, and K. V. Kheruntsyan, Phys. Rev. A 85, 031604(R) (2012).
https://doi.org/10.1103/PhysRevA.85.031604
[49] J. Catani et al., Phys. Rev. A 85, 023623 (2012).
https://doi.org/10.1103/PhysRevA.85.023623
[50] G. Pagano, M. Mancini, G. Cappellini, P. Lombardi, F. Schäfer, H. Hu, X.-J. Liu, J. Catani, C. Sias, M. Inguscio, L. Fallani, Nature Physics 10, 198-201 (2014).
https://doi.org/10.1038/nphys2878
[51] M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch and C. Gross, Science 353, 1257 (2016).
https://doi.org/10.1126/science.aag1635
[52] P. Zupancic, P. M. Preiss, R. Ma, A. Lukin, M. Eric Tai, M. Rispoli, R. Islam, and M. Greiner, Opt. Expr. 24, 13881 (2016).
https://doi.org/10.1364/OE.24.013881
[53] C. Weitenberg: Fluorescence Imaging of Quantum Gases. In Quantum Gas Experiments, vol. Volume 3 of Cold Atoms, pp. 121-143 (Imperial College Press) (2014).
https://doi.org/10.1142/9781783264766_0007
[54] M. J. Bremner et al. Phys. Rev. Lett. 89, 247902 (2002).
https://doi.org/10.1103/PhysRevLett.89.247902
[55] C. N. Yang, Phys. Rev. Lett. 19, 1312 (1967).
https://doi.org/10.1103/PhysRevLett.19.1312
[56] W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
https://doi.org/10.1103/PhysRevLett.80.2245
[57] L. Amico, A., Osterloh, F., Plastina, R., Fazio, G. M Palma, Physical Review A, 69(2), 022304, (2004).
https://doi.org/10.1103/PhysRevA.69.022304
[58] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972), page 298.
[59] B. Gaveau, L. S. Schulman, Journal of Physics A: Mathematical and General, 19(10), 1833, (1986).
https://doi.org/10.1088/0305-4470/19/10/024
[60] M. Olshanii, Phys. Rev. Lett. 81, 938 (1998).
https://doi.org/10.1103/PhysRevLett.81.938
[61] L. Rutherford, J. Goold, Th. Busch and J. F. McCann, Phys. Rev. A 83, 055601 (2011).
https://doi.org/10.1103/PhysRevA.83.055601
[62] A. Sommer, M. Ku, G. Roati and M. W. Zwierlein, Nature 472, 201 (2011).
https://doi.org/10.1038/nature09989
[63] F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, Phys. Rev. X 4, 021034 (2014).
https://doi.org/10.1103/PhysRevX.4.021034
[64] M. Gaudin, The Bethe Wavefunction, Cambridge University Press (2014).
[65] W. Krauth, Phys. Rev. B 44, 9772(R) (1991).
https://doi.org/10.1103/PhysRevB.44.9772
[66] M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices, Oxford University Press (2012).
[67] C. Weitenberg et al., Nature 471, 319 (2011).
https://doi.org/10.1038/nature09827
[68] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
https://doi.org/10.1103/PhysRevLett.81.3108
[69] J. Weiner et al., Rev. Mod. Phys. 71,1 (1999).
https://doi.org/10.1103/RevModPhys.71.1
[70] M. Egorov et al., Phys. Rev. A 87, 053614 (2013).
https://doi.org/10.1103/PhysRevA.87.053614
[71] A. Marte et al., Phys. Rev. Lett. 89, 283202 (2002).
https://doi.org/10.1103/PhysRevLett.89.283202
[72] I. Bloch, Nature 1, 23 (2005).
https://doi.org/10.1038/nphys138
[73] W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, M. Greiner, Nature 462, 74 (2009).
https://doi.org/10.1038/nature08482
[74] D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005).
https://doi.org/10.1016/j.aop.2004.09.010
[75] L. Banchi, T. J. G. Apollaro, A. Cuccoli, R. Vaia, P. Verrucchi, New. J. Phys 13, 123006 (2011).
https://doi.org/10.1088/1367-2630/13/12/123006
[76] Yoav Lahini, Gregory R. Steinbrecher, Adam D. Bookatz, Dirk Englund, arXiv:1501.04349.
arXiv:1501.04349
[77] E. Compagno, L. Banchi, and S. Bose, Phys. Rev. A 92, 022701 (2015).
https://doi.org/10.1103/PhysRevA.92.022701
[78] E. Compagno, L. Banchi, C. Gross, S. Bose, Phys. Rev. A 95, 012307 (2017).
https://doi.org/10.1103/PhysRevA.95.012307
[79] Y. Zhang, Quantum Inf Process, 12:631 (2013).
https://doi.org/10.1007/s11128-012-0409-4
[80] Y. Zhang, Quantum Inf Process, 11:585 (2012).
https://doi.org/10.1007/s11128-011-0268-4
Cited by
On Crossref's cited-by service no data on citing works was found (last attempt 2024-08-21 20:22:01). On SAO/NASA ADS no data on citing works was found (last attempt 2024-08-21 20:22:01).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.