Authors

Diego González Olivares, Borja Peropadre, Alán Aspuru-Guzik, Juan José García-Ripoll

Abstract

In this work we study a system that consists of \( 2M \) matter qubits that interact through a boson sampling circuit, i.e., an \( M \)-port interferometer, embedded in two different architectures. We prove that, under the conditions required to derive a master equation, the qubits evolve according to effective bipartite \( XY \) spin Hamiltonians, with or without local and collective dissipation terms. This opens the door to the simulation of any bipartite spin or hard-core boson models and exploring dissipative phase transitions as the competition between coherent and incoherent exchange of excitations. We also show that in the purely dissipative regime this model has a large number of exact and approximate dark states, whose structure and decay rates can be estimated analytically. We finally argue that this system may be used for the adiabatic preparation of boson sampling states encoded in the matter qubits.

Citation

  • Journal: Physical Review A
  • Year: 2016
  • Volume: 94
  • Issue: 2
  • Pages:
  • Publisher: American Physical Society (APS)
  • DOI: 10.1103/physreva.94.022319

BibTeX

@article{Gonz_lez_Olivares_2016,
  title={{Quantum simulation with a boson sampling circuit}},
  volume={94},
  ISSN={2469-9934},
  DOI={10.1103/physreva.94.022319},
  number={2},
  journal={Physical Review A},
  publisher={American Physical Society (APS)},
  author={González Olivares, Diego and Peropadre, Borja and Aspuru-Guzik, Alán and García-Ripoll, Juan José},
  year={2016}
}

Download the bib file

References

  • Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994) – 10.1103/physrevlett.73.58
  • Lund-Hansen, T. et al. Experimental Realization of Highly Efficient Broadband Coupling of Single Quantum Dots to a Photonic Crystal Waveguide. Phys. Rev. Lett. 101, (2008) – 10.1103/physrevlett.101.113903
  • Goban, A. et al. Atom–light interactions in photonic crystals. Nat Commun 5, (2014) – 10.1038/ncomms4808
  • Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-Silicon Waveguide Quantum Circuits. Science 320, 646–649 (2008) – 10.1126/science.1155441
  • Meany, T. et al. Laser written circuits for quantum photonics. Laser & Photonics Reviews 9, 363–384 (2015) – 10.1002/lpor.201500061
  • Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015) – 10.1126/science.aab3642
  • Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015) – 10.1103/revmodphys.87.347
  • Tiecke, T. G. et al. Nanophotonic quantum phase switch with a single atom. Nature 508, 241–244 (2014) – 10.1038/nature13188
  • Chang, D. E., Sørensen, A. S., Hemmer, P. R. & Lukin, M. D. Quantum Optics with Surface Plasmons. Phys. Rev. Lett. 97, (2006) – 10.1103/physrevlett.97.053002
  • Gonzalez-Tudela, A. et al. Entanglement of Two Qubits Mediated by One-Dimensional Plasmonic Waveguides. Phys. Rev. Lett. 106, (2011) – 10.1103/physrevlett.106.020501
  • S. Aaronson, Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (2011)
  • B. T. Gard, From Atomic to Mesoscale (2015)
  • Broome, M. A. et al. Photonic Boson Sampling in a Tunable Circuit. Science 339, 794–798 (2013) – 10.1126/science.1231440
  • Spring, J. B. et al. Boson Sampling on a Photonic Chip. Science 339, 798–801 (2013) – 10.1126/science.1231692
  • Tillmann, M. et al. Experimental boson sampling. Nature Photon 7, 540–544 (2013) – 10.1038/nphoton.2013.102
  • Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nature Photon 7, 545–549 (2013) – 10.1038/nphoton.2013.112
  • Shen, C., Zhang, Z. & Duan, L.-M. Scalable Implementation of Boson Sampling with Trapped Ions. Phys. Rev. Lett. 112, (2014) – 10.1103/physrevlett.112.050504
  • Motes, K. R., Gilchrist, A., Dowling, J. P. & Rohde, P. P. Scalable Boson Sampling with Time-Bin Encoding Using a Loop-Based Architecture. Phys. Rev. Lett. 113, (2014) – 10.1103/physrevlett.113.120501
  • Motes, K. R. et al. Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit. Phys. Rev. Lett. 114, (2015) – 10.1103/physrevlett.114.170802
  • Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R. & Aspuru-Guzik, A. Boson sampling for molecular vibronic spectra. Nature Photon 9, 615–620 (2015) – 10.1038/nphoton.2015.153
  • Hoffmann, E. et al. A superconducting 180° hybrid ring coupler for circuit quantum electrodynamics. Applied Physics Letters 97, (2010) – 10.1063/1.3522650
  • Kurcz, A., Bermudez, A. & García-Ripoll, J. J. Hybrid Quantum Magnetism in Circuit QED: From Spin-Photon Waves to Many-Body Spectroscopy. Phys. Rev. Lett. 112, (2014) – 10.1103/physrevlett.112.180405
  • Díaz-Camacho, G., Bermudez, A. & García-Ripoll, J. J. Dynamical polaronAnsatz: A theoretical tool for the ultrastrong-coupling regime of circuit QED. Phys. Rev. A 93, (2016) – 10.1103/physreva.93.043843
  • Rossini, D. & Fazio, R. Mott-Insulating and Glassy Phases of Polaritons in 1D Arrays of Coupled Cavities. Phys. Rev. Lett. 99, (2007) – 10.1103/physrevlett.99.186401
  • Falci, G., Fazio, R., Palma, G. M., Siewert, J. & Vedral, V. Detection of geometric phases in superconducting nanocircuits. Nature 407, 355–358 (2000) – 10.1038/35030052
  • Nissen, F. et al. Nonequilibrium Dynamics of Coupled Qubit-Cavity Arrays. Phys. Rev. Lett. 108, (2012) – 10.1103/physrevlett.108.233603
  • Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nature Phys 11, 124–130 (2015) – 10.1038/nphys3215
  • González-Tudela, A. & Porras, D. Mesoscopic Entanglement Induced by Spontaneous Emission in Solid-State Quantum Optics. Phys. Rev. Lett. 110, (2013) – 10.1103/physrevlett.110.080502