Efficient quantum simulation of fermionic and bosonic models in trapped ions

Feynman RP: Simulating physics with computers. Int. J. Theor. Phys. 1982, 21: 467. 10.1007/BF02650179

Lloyd S: Universal quantum simulators. Science 1996, 273: 1073. 10.1126/science.273.5278.1073

Buluta I, Nori F: Quantum simulators. Science 2009, 326: 108. 10.1126/science.1177838

Johanning M, Varón AF, Wunderlich C: Quantum simulations with cold trapped ions. J. Phys. B 2009., 42: Article ID 154009 Article ID 154009

Schneider C, Porras D, Schaetz T: Experimental quantum simulations of many-body physics with trapped ions. Rep. Prog. Phys. 2012., 75: Article ID 024401 Article ID 024401

Jané E, Vidal G, Dür W, Zoller P, Cirac JI: Simulation of quantum dynamics with quantum optical systems. Quantum Inf. Comput. 2003, 3: 15.

Porras D, Cirac JI: Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 2004., 92: Article ID 207901 Article ID 207901

Friedenauer A, Schmitz H, Glueckert JT, Porras D, Schätz T: Simulating a quantum magnet with trapped ions. Nat. Phys. 2008, 4: 757. 10.1038/nphys1032

Kim K, Chang M-S, Korenblit S, Islam R, Edwards EE, Freericks JK, Lin G-D, Duan L-M, Monroe C: Quantum simulation of frustrated Ising spins with trapped ions. Nature 2010, 465: 590. 10.1038/nature09071

Greiner M, Mandel O, Esslinger T, Hänsch TW, Bloch I: Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 2002, 415: 39. 10.1038/415039a

Lanyon BP, Whitfield JD, Gillett GG, Goggin ME, Almeida MP, Kassal I, Biamonte JD, Mohseni M, Powell BJ, Barbieri M, Aspuru-Guzik A, White AG: Towards quantum chemistry on a quantum computer. Nat. Chem. 2010, 2: 106. 10.1038/nchem.483

Matthews JCF, Poulios K, Meinecke JDA, Politi A, Peruzzo A, Ismail N, Wörhoff K, Thompson MG, O’Brien JL: Observing fermionic statistics with photons in arbitrary processes. Sci. Rep. 2013, 3: 1539.

Crespi A, Osellame R, Ramponi R, Giovannetti V, Fazio R, Sansoni L, Nicola FD, Sciarrino F, Mataloni P: Anderson localization of entangled photons in an integrated quantum walk. Nat. Photonics 2013, 7: 322. 10.1038/nphoton.2013.26

Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R: Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 2012., 108: Article ID 010502 Article ID 010502

Weimer H, Müller M, Lesanovsky I, Zoller P, Büchler HP: A Rydberg quantum simulator. Nat. Phys. 2010, 6: 382. 10.1038/nphys1614

Lamata L, León J, Schätz T, Solano E: Dirac equation and quantum relativistic effects in a single trapped ion. Phys. Rev. Lett. 2007., 98: Article ID 253005 Article ID 253005

Gerritsma R, Kirchmair G, Zähringer F, Solano E, Blatt R, Roos CF: Quantum simulation of the Dirac equation. Nature 2010, 463: 68. 10.1038/nature08688

Casanova J, García-Ripoll JJ, Gerritsma R, Roos CF, Solano E: Klein tunneling and Dirac potentials in trapped ions. Phys. Rev. A 2010., 82: Article ID 020101 Article ID 020101

Gerritsma R, Lanyon BP, Kirchmair G, Zähringer F, Hempel C, Casanova J, García-Ripoll JJ, Solano E, Blatt R, Roos CF: Quantum simulation of the Klein paradox with trapped ions. Phys. Rev. Lett. 2011., 106: Article ID 060503 Article ID 060503

Casanova J, Lamata L, Egusquiza IL, Gerritsma R, Roos CF, García-Ripoll JJ, Solano E: Quantum simulation of quantum field theories in trapped ions. Phys. Rev. Lett. 2011., 107: Article ID 260501 Article ID 260501

Hauke P, Marcos D, Dalmonte M, Zoller P: Quantum simulation of a lattice Schwinger model in a chain of trapped ions. Phys. Rev. X 2013., 3: Article ID 041018 Article ID 041018

Casanova J, Mezzacapo A, Lamata L, Solano E: Quantum simulation of interacting fermion lattice models in trapped ions. Phys. Rev. Lett. 2012., 108: Article ID 190502 Article ID 190502

Mezzacapo A, Casanova J, Lamata L, Solano E: Digital quantum simulation of the Holstein model in trapped ions. Phys. Rev. Lett. 2012., 109: Article ID 200501 Article ID 200501

Yung M-H, Casanova J, Mezzacapo A, McClean J, Lamata L, Aspuru-Guzik A, Solano E: From transistor to trapped-ion computers for quantum chemistry. Sci. Rep. 2014, 4: 3589.

Brown LS, Gabrielse G: Geonium theory: physics of a single electron or ion in a Penning trap. Rev. Mod. Phys. 1986, 58: 233. 10.1103/RevModPhys.58.233

Leibfried D, Blatt R, Monroe C, Wineland D: Quantum dynamics of single trapped ions. Rev. Mod. Phys. 2003, 75: 281. 10.1103/RevModPhys.75.281

Cirac JI, Zoller P: Quantum computations with cold trapped ions. Phys. Rev. Lett. 1995, 74: 4091. 10.1103/PhysRevLett.74.4091

Mølmer K, Sørensen A: Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 1999, 82: 1835. 10.1103/PhysRevLett.82.1835

Mezzacapo A, Lamata L, Filipp S, Solano E: Many-body interactions with tunable-coupling transmon qubits. arXiv:1403.3652.

Las Heras U, Mezzacapo A, Lamata L, Filipp S, Wallraff A, Solano E: Digital quantum simulation of spin systems in superconducting circuits. Phys. Rev. Lett. 2014., 112: Article ID 200501 Article ID 200501

Mezzacapo A, Las Heras U, Pedernales JS, DiCarlo L, Solano E, Lamata L: Digital quantum Rabi and Dicke models in superconducting circuits. arXiv:1405.5814.

Holstein T: Studies of polaron motion: Part I. The molecular-crystal model. Ann. Phys. 1959, 8: 325. 10.1016/0003-4916(59)90002-8

Peskin ME, Schroeder DV: Quantum Field Theory. Addison-Wesley, Reading; 1995.

Garcia-Ripoll JJ, Zoller P, Cirac JI: Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. Phys. Rev. Lett. 2003., 91: Article ID 157901 Article ID 157901

Duan L-M: Scaling ion trap quantum computation through fast quantum gates. Phys. Rev. Lett. 2004., 93: Article ID 100502 Article ID 100502

Kielpinski D, Monroe C, Wineland DJ: Architecture for a large-scale ion-trap quantum computer. Nature 2002, 417: 709. 10.1038/nature00784

Nielsen MA, Chuang IL: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge; 2000.

Cetina M, Bylinskii A, Karpa L, Gangloff D, Beck KM, Ge Y, Scholz M, Grier AT, Chuang I, Vuletić V: One-dimensional array of ion chains coupled to an optical cavity. New J. Phys. 2013., 15: Article ID 053001 Article ID 053001

Lamata L, Leibrandt DR, Chuang IL, Cirac JI, Lukin MD, Vuletić V, Yelin SF: Ion crystal transducer for strong coupling between single ions and single photons. Phys. Rev. Lett. 2011., 107: Article ID 030501 Article ID 030501

Lanyon BP, Hempel C, Nigg D, Müller M, Gerritsma R, Zähringer F, Schindler P, Barreiro JT, Rambach M, Kirchmair G, Hennrich M, Zoller P, Blatt R, Roos CF: Universal digital quantum simulation with trapped ions. Science 2011, 334: 57. 10.1126/science.1208001

Kim K, Korenblit S, Islam R, Edwards EE, Chang M-S, Noh C, Carmichael H, Lin G-D, Duan L-M, Wang CCJ, Freericks JK, Monroe C: Quantum simulation of the transverse Ising model with trapped ions. New J. Phys. 2011., 13: Article ID 105003 Article ID 105003

Kirchmair G, Benhelm J, Zähringer F, Gerritsma R, Roos CF, Blatt R: Deterministic entanglement of ions in thermal states of motion. New J. Phys. 2009., 11: Article ID 023002 Article ID 023002

Wecker D, Bauer B, Clark BK, Hastings MB, Troyer M: Can quantum chemistry be performed on a small quantum computer? arXiv:1312.1695.