R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics, vol.21, pp.467-488, 1982.

A. Trabesinger, Quantum simulation, Nature Physics, vol.8, pp.263-263, 2012.

D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Physical Review Letters, vol.48, pp.1559-1562, 1982.

R. B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Physical Review Letters, vol.50, pp.1395-1398, 1983.

F. D. Haldane, Model for a Quantum Hall Effect without Landau Levels: CondensedMatter Realization of the "Parity Anomaly, Physical Review Letters, vol.61, pp.2015-2018, 1988.

N. Regnault and B. A. Bernevig, Fractional Chern Insulator, Physical Review X, vol.1, p.21014, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00649047

S. Schmidt and J. Koch, Circuit QED lattices: Towards quantum simulation with superconducting circuits: Circuit QED lattices, Annalen der Physik, vol.525, pp.395-412, 2013.

K. L. Hur, L. Henriet, A. Petrescu, K. Plekhanov, G. Roux et al., Manybody quantum electrodynamics networks: Non-equilibrium condensed matter physics with light, Comptes Rendus Physique, vol.17, pp.808-835, 2016.
URL : https://hal.archives-ouvertes.fr/cea-01228030

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, Time-reversal-symmetry breaking in circuit-QED-based photon lattices, Physical Review A -Atomic, Molecular, and Optical Physics, vol.82, pp.1-18, 2010.

J. Koch and K. L. Hur, Superfluid-Mott-insulator transition of light in the JaynesCummings lattice, Physical Review A, vol.80, p.23811, 2009.

A. Blais, R. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Physical Review A, vol.69, p.62320, 2004.

M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting Qubits: A Short Review, 2004.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster et al., Charge-insensitive qubit design derived from the Cooper pair box, Physical Review A, vol.76, p.42319, 2007.

V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets, Science, vol.326, pp.113-116, 2009.

J. M. Chow, J. M. Gambetta, A. D. Córcoles, S. T. Merkel, J. A. Smolin et al., Universal Quantum Gate Set Approaching Fault-Tolerant Thresholds with Superconducting Qubits, vol.109, p.60501, 2012.

M. H. Devoret and R. J. Schoelkopf, Superconducting Circuits for Quantum Information: An Outlook, Science, vol.339, pp.1169-1174, 2013.

M. Fitzpatrick, N. M. Sundaresan, A. C. Li, J. Koch, and A. A. Houck, Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice, Physical Review X, vol.7, p.11016, 2017.

P. Roushan, C. Neill, A. Megrant, Y. Chen, R. Babbush et al., Chiral ground-state currents of interacting photons in a synthetic magnetic field, Nature Physics, vol.13, pp.146-151, 2017.

P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant et al., Spectroscopic signatures of localization with interacting photons in superconducting qubits, Science, vol.358, pp.1175-1179, 2017.

R. Ma, B. Saxberg, C. Owens, N. Leung, Y. Lu et al., A Dissipatively Stabilized Mott Insulator of Photons, 2018.

L. Lu, J. D. Joannopoulos, and M. Soljav, Topological photonics, Nature Photonics, vol.8, pp.821-829, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02378333

A. B. Khanikaev and G. Shvets, Two-dimensional topological photonics, Nature Photonics, vol.11, pp.763-773, 2017.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi et al., Topological Photonics, 2018.

M. Kohmoto, Topological invariant and the quantization of the Hall conductance, Annals of Physics, vol.160, pp.343-354, 1985.

C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Physical Review Letters, vol.95, p.226801, 2005.

C. L. Kane and E. J. Mele, Z 2 Topological Order and the Quantum Spin Hall Effect, Physical Review Letters, vol.95, p.146802, 2005.

B. A. Bernevig and S. Zhang, Quantum Spin Hall Effect, Physical Review Letters, vol.96, p.106802, 2006.

B. I. Halperin, Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Physical Review B, vol.25, pp.2185-2190, 1982.

M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Physical Review B, vol.38, pp.9375-9389, 1988.

L. Fidkowski, T. S. Jackson, and I. Klich, Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions, Physical Review Letters, vol.107, p.36601, 2011.

R. S. Mong and V. Shivamoggi, Edge states and the bulk-boundary correspondence in Dirac Hamiltonians, Physical Review B, vol.83, p.125109, 2011.

T. Fukui, K. Shiozaki, T. Fujiwara, and S. Fujimoto, Bulk-Edge Correspondence for Chern Topological Phases: A Viewpoint from a Generalized Index Theorem, Journal of the Physical Society of Japan, vol.81, p.114602, 2012.

A. B. Khanikaev, S. Mousavi, W. Tse, M. Kargarian, A. H. Macdonald et al., Photonic topological insulators, Nature Materials, vol.12, pp.233-239, 2013.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky et al., Photonic Floquet topological insulators, vol.496, pp.196-200, 2013.

M. Hafezi, E. Demler, M. Lukin, and J. Taylor, Robust optical delay lines via topological protection, Nature Physics, vol.7, pp.907-912, 2011.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nature Photonics, vol.7, pp.1001-1005, 2013.

H. Wang, M. Hofheinz, J. Wenner, M. Ansmann, R. C. Bialczak et al., Improving the coherence time of superconducting coplanar resonators, Physics Letters, vol.95, p.233508, 2009.

C. Owens, A. Lachapelle, B. Saxberg, B. M. Anderson, R. Ma et al., Quarter-Flux Hofstadter Lattice in Qubit-Compatible Microwave Cavity Array, Physical Review A, vol.97, p.13818, 2018.

J. Ningyuan, C. Owens, A. Sommer, D. Schuster, and J. Simon, Time-and SiteResolved Dynamics in a Topological Circuit, Physical Review X, vol.5, p.21031, 2015.

M. Mili?evi?, T. Ozawa, P. Andreakou, I. Carusotto, T. Jacqmin et al., Edge states in polariton honeycomb lattices, 2D Materials, vol.2, p.34012, 2015.

M. Mili?evi?, T. Ozawa, G. Montambaux, I. Carusotto, E. Galopin et al., Orbital Edge States in a Photonic Honeycomb Lattice, Physical Review Letters, vol.118, p.107403, 2017.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov et al., Direct Observation of Dirac Cones and a Flatband in a Honeycomb Lattice for Polaritons, Physical Review Letters, vol.112, p.116402, 2014.

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H. Stöckmann, T. Hossain et al., Dirac point and edge states in a microwave realization of tight-binding graphene-like structures, Physical Review B, vol.82, p.94308, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00489474

M. Bellec, U. Kuhl, G. Montambaux, and F. Mortessagne, Tight-binding couplings in microwave artificial graphene, Physical Review B, vol.88, p.115437, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00843999

S. Yves, F. Lemoult, M. Fink, and G. Lerosey, Crystalline Soda Can Metamaterial exhibiting Graphene-like Dispersion at subwavelength scale, 2017.

M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale et al., Engineering artificial graphene in a two-dimensional electron gas, Physical Review B, vol.79, p.241406, 2009.

M. C. Rechtsman, J. M. Zeuner, A. Tünnermann, S. Nolte, M. Segev et al., Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures, Nature Photonics, vol.7, pp.153-158, 2013.

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen et al., Topological Creation and Destruction of Edge States in Photonic Graphene, Physical Review Letters, vol.111, p.103901, 2013.

M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-leija, A. Szameit et al., Topological protection of photonic path entanglement, Optica, vol.3, p.925, 2016.

S. Wang, D. Scarabelli, L. Du, Y. Y. Kuznetsova, L. N. Pfeiffer et al., Observation of Dirac bands in artificial graphene in small-period nanopatterned GaAs quantum wells, Nature Nanotechnology, vol.13, pp.29-33, 2018.

B. Dietz and A. Richter, From graphene to fullerene: experiments with microwave photonic crystals, Physica Scripta, vol.94, p.14002, 2019.

J. C. Culbertson, H. S. Newman, and C. Wilker, Optical probe of microwave current distributions in high temperature superconducting transmission lines, Journal of Applied Physics, vol.84, pp.2768-2787, 1998.

A. P. Zhuravel, C. Kurter, A. V. Ustinov, and S. M. Anlage, Unconventional rf photoresponse from a superconducting spiral resonator, Physical Review B, vol.85, p.134535, 2012.

A. S. Averkin, A. P. Zhuravel, A. Karpov, S. M. Anlage, and A. V. Ustinov, Ultracompact superconductive resonator with double-spiral structure, 2013 7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, pp.142-144, 2013.

G. W. Semenoff, V. Semenoff, and F. Zhou, Domain Walls in Gapped Graphene, Physical Review Letters, vol.101, p.87204, 2008.

B. Bernevig, T. Hughes, and B. Bernevig, Topological Insulators and Topological Superconductors, 2013.

P. Soltan-panahi, J. Struck, P. Hauke, A. Bick, W. Plenkers et al., Multi-component quantum gases in spin-dependent hexagonal lattices, Nature Physics, vol.7, pp.434-440, 2011.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, vol.483, pp.302-305, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00820435

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, Artificial honeycomb lattices for electrons, atoms and photons, Nature Nanotechnology, vol.8, pp.625-633, 2013.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult et al., Crystalline metamaterials for topological properties at subwavelength scales, Nature Communications, vol.8, p.16023, 2017.
URL : https://hal.archives-ouvertes.fr/cea-01571409

H. Wang, A. P. Zhuravel, S. Indrajeet, B. G. Taketani, M. D. Hutchings et al., Mode Structure in Superconducting Metamaterial Transmission Line Resonators, 2018.

G. W. Semenoff, Condensed-Matter Simulation of a Three-Dimensional Anomaly, Physical Review Letters, vol.53, pp.2449-2452, 1984.

E. Akkermans and G. Montambaux, Mesoscopic physics of electrons and photons, vol.OCLC, p.174557159, 2007.

S. Ryu and Y. Hatsugai, Topological Origin of Zero-Energy Edge States in ParticleHole Symmetric Systems, Physical Review Letters, vol.89, p.77002, 2002.

P. Delplace, D. Ullmo, and G. Montambaux, Zak phase and the existence of edge states in graphene, Physical Review B, vol.84, p.195452, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00644295

M. Bellec, U. Kuhl, G. Montambaux, and F. Mortessagne, Manipulation of edge states in microwave artificial graphene, New Journal of Physics, vol.16, p.113023, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01011880

J. , Introduction to Dirac materials and topological insulators, Comptes Rendus Physique, vol.14, pp.760-778, 2013.

J. Fuchs and M. O. Goerbig, Introduction to the Physical Properties of Graphene, 2008.

S. Ryu, C. Mudry, C. Hou, and C. Chamon, Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics, Physical Review B, vol.80, p.205319, 2009.

Y. Liu, C. Lian, Y. Li, Y. Xu, and W. Duan, Pseudospins and Topological Effects of Phonons in a Kekulé Lattice, Physical Review Letters, vol.119, p.255901, 2017.

W. Yao, S. A. Yang, and Q. Niu, Edge States in Graphene: From Gapped Flat-Band to Gapless Chiral Modes, Physical Review Letters, vol.102, p.96801, 2009.
DOI : 10.1103/physrevlett.102.096801
URL : http://arxiv.org/pdf/0810.2101

V. V. Albert, L. I. Glazman, and J. Liang, Topological Properties of Linear Circuit Lattices, Physical Review L, vol.114, p.173902, 2015.
DOI : 10.1103/physrevlett.114.173902
URL : https://link.aps.org/accepted/10.1103/PhysRevLett.114.173902

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, Metamaterial tuning by manipulation of near-field interaction, Physical Review B, vol.82, p.155128, 2010.
DOI : 10.1103/physrevb.82.155128
URL : https://idus.us.es/xmlui/bitstream/11441/58795/1/Metamaterial%20tuning.pdf

V. Lomanets, O. Zhuromskyy, G. Onishchukov, and U. Peschel, Electrical circuit model of arrays of resonant elements, Physical Review B, vol.85, p.125110, 2012.
DOI : 10.1103/physrevb.85.125110

S. Y. Elnaggar, R. Tervo, and S. M. Mattar, Energy Coupled Mode Theory for an arbitrary number of resonators, IEEE Transactions on Microwave Theory and Techniques, vol.63, pp.2115-2123, 2015.
DOI : 10.1109/tmtt.2015.2434377
URL : http://arxiv.org/pdf/1305.6085

J. D. Jackson, Classical electrodynamics, 1975.

D. L. Underwood, W. E. Shanks, A. C. Li, L. Ateshian, J. Koch et al., Imaging Photon Lattice States by Scanning Defect Microscopy, Physical Review X, vol.6, p.21044, 2016.
DOI : 10.1103/physrevx.6.021044
URL : http://link.aps.org/pdf/10.1103/PhysRevX.6.021044

A. P. Zhuravel, A. G. Sivakov, O. G. Turutanov, A. N. Omelyanchouk, S. M. Anlage et al., Laser scanning microscopy of HTS films and devices (Review Article), Low Temperature Physics, vol.32, pp.592-607, 2006.
DOI : 10.1063/1.2215376
URL : http://arxiv.org/pdf/cond-mat/0512582

J. Gao, The Physics of Superconducting Microwave Resonators

D. P. Pappas, M. R. Vissers, D. S. Wisbey, J. S. Kline, and J. Gao, Two Level System Loss in Superconducting Microwave Resonators, IEEE Transactions on Applied Superconductivity, vol.21, pp.871-874, 2011.
DOI : 10.1109/tasc.2010.2097578

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, Observation of Photonic Topological Valley Hall Edge States, Physical Review Letters, vol.120, p.63902, 2018.

V. M. Pereira, F. Guinea, J. M. Lopes-dos-santos, N. M. Peres, and A. H. Castro-neto, Disorder Induced Localized States in Graphene, Physical Review Letters, vol.96, p.36801, 2006.
DOI : 10.1103/physrevlett.96.036801
URL : http://arxiv.org/pdf/cond-mat/0508530

A. Karpov, A. P. Zhuravel, A. S. Averkin, V. I. Chichkov, and A. V. Ustinov, Phasesensitive imaging of microwave currents in superconductive circuits, 2018.

M. Masir, D. Moldovan, and F. Peeters, Pseudo magnetic field in strained graphene: Revisited, Solid State Communications 175-176, pp.76-82, 2013.

C. Poli, J. Arkinstall, and H. Schomerus, Degeneracy doubling and sublattice polarization in strain-induced pseudo-Landau levels, Physical Review B, vol.90, p.155418, 2014.
DOI : 10.1103/physrevb.90.155418
URL : http://eprints.lancs.ac.uk/73420/1/PhysRevB.90.155418.pdf

G. Salerno, T. Ozawa, H. M. Price, and I. Carusotto, Propagating edge states in strained honeycomb lattices, Physical Review B, vol.95, p.245418, 2017.
DOI : 10.1103/physrevb.95.245418
URL : http://arxiv.org/pdf/1702.02336

K. Fang, Z. Yu, and S. Fan, Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nature Photonics, vol.6, pp.782-787, 2012.

J. Basset, D. Watfa, G. Aiello, M. Féchant, A. Morvan et al., Non-linear Hybrid Microwave Resonators Made by He-Beam Assisted Deposition of Tungsten Nanowires, 2018.
DOI : 10.1063/1.5080925

L. Grünhaupt, M. Spiecker, D. Gusenkova, N. Maleeva, S. T. Skacel et al., Granular aluminum: A superconducting material for high impedance quantum circuits, 2018.

D. Niepce, J. Burnett, and J. Bylander, High Kinetic Inductance NbN Nanowire Superinductors, 2018.