H. Charles, G. Bennett, and . Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoretical Computer Science, vol.560, pp.7-11, 2014.

L. Davidovich, Towards the ultimate precision limits: An introduction to quantum metrology, pp.2019-2023, 2016.

T. Symul, S. M. Assad, and P. K. Lam, Real time demonstration of high bitrate quantum random number generation with coherent laser light, Applied Physics Letters, vol.98, issue.23, p.231103, 2011.

P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing, vol.26, issue.5, pp.1484-1509, 1997.

Y. Nakamura, C. D. Chen, and J. S. Tsai, Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by josephson coupling, Physical Review Letters, vol.79, issue.12, pp.2328-2331, 1997.

D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier et al., Manipulating the quantum state of an electrical circuit, Science, vol.296, issue.5569, pp.886-889, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00021251

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani et al., Observation of high coherence in josephson junction qubits measured in a three-dimensional circuit QED architecture, Physical Review Letters, vol.107, issue.24, 2011.

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. Plourde, J. M. Chow et al., Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms, Physical Review B, vol.86, issue.10, 2012.

A. P. Sears, Extending Coherence in Superconducting Qubits: From microseconds to milliseconds, 2013.

K. L. Geerlings, Improving Coherence of Superconducting Qubitsand Resonators, 2013.

M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science, vol.339, issue.6124, pp.1169-1174, 2013.

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, issue.6, 2004.

Y. Makhlin, G. Schön, and A. Shnirman, Quantum-state engineering with josephson-junction devices, Reviews of Modern Physics, vol.73, issue.2, pp.357-400, 2001.

S. M. Girvin, Circuit QED: superconducting qubits coupled to microwave photons, Quantum Machines: Measurement and Control of Engineered Quantum Systems, pp.113-256, 2014.

S. O. Mundhada, S. Shankar, A. Narla, E. Zalys-geller, S. M. Girvin et al., Dependence of transmon qubit relaxation rate on readout drive power, vol.61, 2016.

M. Mirrahimi, Z. Leghtas, V. Albert, S. Touzard, R. Schoelkopf et al., Dynamically protected cat-qubits: a new paradigm for universal quantum computation, New Journal of Physics, vol.16, issue.4, p.45014, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01089514

M. H. Devoret, Quantum Fluctuations in Electrical Circuits, Fluctuations Quantiques/Quantum Fluctuations, p.351, 1997.

W. H. Louisell, A. Yariv, and A. E. Siegman, Quantum fluctuations and noise in parametric processes. i, Physical Review, vol.124, issue.6, pp.1646-1654, 1961.

M. Mirrahimi and P. Rouchon, Dynamics and control of open quantum systems, pp.2018-2021

A. Roy and M. Devoret, Introduction to parametric amplification of quantum signals with josephson circuits, Comptes Rendus Physique, vol.17, issue.7, pp.740-755, 2016.

B. Yurke, L. R. Corruccini, P. G. Kaminsky, L. W. Rupp, A. D. Smith et al., Observation of parametric amplification and deamplification in a josephson parametric amplifier, Physical Review A, vol.39, issue.5, pp.2519-2533, 1989.

M. A. Castellanos-beltran and K. W. Lehnert, Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator, Applied Physics Letters, vol.91, issue.8, p.83509, 2007.

T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki et al., Flux-driven josephson parametric amplifier, Applied Physics Letters, vol.93, issue.4, p.42510, 2008.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan et al., Phase-preserving amplification near the quantum limit with a josephson ring modulator, Nature, vol.465, issue.7294, pp.64-68, 2010.

F. D. Schackert, A Practical Quantum-Limited Parametric Amplifier Based on the Josephson Ring Modulator, 2013.

E. Flurin, The Josephson Mixer, a Swiss army knife for microwave quantum optics. Theses, Ecole Normale Supérieure, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00910066

E. Flurin, N. Roch, J. D. Pillet, F. Mallet, and B. Huard, Superconducting quantum node for entanglement and storage of microwave radiation, Physical Review Letters, vol.114, issue.9, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01079032

Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis et al., Confining the state of light to a quantum manifold by engineered two-photon loss, Science, vol.347, issue.6224, pp.853-857, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01240210

. S-o-mundhada, S. Grimm, . Touzard, . Vool, M. Shankar et al., Generating higher-order quantum dissipation from lower-order parametric processes, Quantum Science and Technology, vol.2, p.24005, 2017.

C. Macklin, K. O'brien, D. Hover, M. E. Schwartz, V. Bolkhovsky et al., A near-quantum-limited josephson traveling-wave parametric amplifier, Science, vol.350, issue.6258, pp.307-310, 2015.

J. Venkatraman, X. Xiao, C. Smith, Z. Leghtas, L. Verney et al., Suppressing the instabilities of the rf driven transmon by a kinetic inductive shunt -part 1: Motivation and modelization, APS March Meeting, Session E26: Driven and Dissipative Superconducting Circuits, 2019.

R. Lescanne, L. Verney, Q. Ficheux, M. H. Devoret, B. Huard et al., Escape of a driven quantum josephson circuit into unconfined states, Physical Review Applied, vol.11, issue.1, 2019.

C. Wang, Y. Y. Gao, I. M. Pop, U. Vool, C. Axline et al., Measurement and control of quasiparticle dynamics in a superconducting qubit, Nature Communications, vol.5, issue.1, 2014.

Y. Y. Gao, B. J. Lester, Y. Zhang, C. Wang, S. Rosenblum et al., Programmable interference between two microwave quantum memories, 2018.

M. Boissonneault, J. M. Gambetta, and A. Blais, Improved superconducting qubit readout by qubit-induced nonlinearities, Phys. Rev. Lett, vol.105, p.100504, 2010.

M. D. Reed, L. Dicarlo, B. R. Johnson, L. Sun, D. I. Schuster et al., High-fidelity readout in circuit quantum electrodynamics using the jaynes-cummings nonlinearity, Phys. Rev. Lett, vol.105, p.173601, 2010.

L. S. Bishop, E. Ginossar, and S. M. Girvin, Response of the strongly driven jaynes-cummings oscillator, Phys. Rev. Lett, vol.105, p.100505, 2010.

M. Elliott and E. Ginossar, Applications of the fokker-planck equation in circuit quantum electrodynamics, Phys. Rev. A, vol.94, p.43840, 2016.

.. K. Th, G. Mavrogordatos, M. Tancredi, M. J. Elliott, A. Peterer et al., Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics, Phys. Rev. Lett, vol.118, p.40402, 2017.

D. Sank, Z. Chen, M. K. , J. Kelly, R. Barends et al., Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation, Physical Review Letters, vol.117, issue.19, 2016.

R. Azouit, Élimination adiabatique pour systèmes quantiques ouverts, Pierre Mathématiques et automatique Paris Sciences et Lettres, 2017.

P. Forni, Third-and fourth-order adiabatic elimination for two-photon-pumping example

A. Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol.452, pp.2551-2577, 1954.

Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret et al., Hardware-efficient autonomous quantum memory protection, Physical Review Letters, vol.111, issue.12, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00924534

J. Cohen, Autonomous quantum error correction with superconducting qubits, Mazyar Physique quantique Paris Sciences et Lettres, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01545186

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. Huang et al., Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature, vol.431, issue.7005, pp.162-167, 2004.

D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta et al., Resolving photon number states in a superconducting circuit, Nature, vol.445, issue.7127, pp.515-518, 2007.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik et al., Observation of quantum state collapse and revival due to the single-photon kerr effect, Nature, vol.495, issue.7440, pp.205-209, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00845264

B. Abdo, K. Sliwa, F. Schackert, N. Bergeal, M. Hatridge et al., Full coherent frequency conversion between two propagating microwave modes, Physical Review Letters, vol.110, issue.17, 2013.

M. A. Castellanos-beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Amplification and squeezing of quantum noise with a tunable josephson metamaterial, Nature Physics, vol.4, issue.12, pp.929-931, 2008.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, Generating entangled microwave radiation over two transmission lines, Physical Review Letters, vol.109, issue.18, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00761350

U. Vool, S. Shankar, S. O. Mundhada, N. Ofek, A. Narla et al., Continuous quantum nondemolition measurement of the transverse component of a qubit, Physical Review Letters, vol.117, p.133601, 2016.

D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R. Huang et al., ac stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field, Phys. Rev. Lett, vol.94, p.123602, 2005.

F. R. Ong, M. Boissonneault, F. Mallet, A. Palacios-laloy, A. Dewes et al., Circuit qed with a nonlinear resonator: ac-stark shift and dephasing, Phys. Rev. Lett, vol.106, p.167002, 2011.

J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio et al., Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting, Phys. Rev. A, vol.74, p.42318, 2006.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster et al., Chargeinsensitive qubit design derived from the cooper pair box, Phys. Rev. A, vol.76, p.42319, 2007.

I. Pietikäinen, S. Danilin, K. S. Kumar, A. Vepsäläinen, D. S. Golubev et al., Observation of the bloch-siegert shift in a driven quantum-toclassical transition, Phys. Rev. B, vol.96, p.20501, 2017.

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and NonMarkovian Quantum Stochastic Methods with Applications to Quantum Optics, 2004.

E. Faou, Geometric Numerical Integration and Schrödinger Equations, 2012.

I. Pietikäinen, S. Danilin, K. S. Kumar, J. Tuorila, and G. S. Paraoanu, Multilevel effects in a driven generalized rabi model, Journal of Low Temperature Physics, vol.191, issue.5-6, pp.354-364, 2018.

S. E. Nigg, H. Paik, B. Vlastakis, G. Kirchmair, S. Shankar et al., Black-box superconducting circuit quantization, Physical Review Letters, vol.108, issue.24, 2012.

M. Grifoni and P. Hänggi, Driven quantum tunneling, Physics Reports, vol.304, issue.5, pp.229-354, 1998.

M. Silveri, J. Tuorila, M. Kemppainen, and E. Thuneberg, Probe spectroscopy of quasienergy states, Physical Review B, vol.87, issue.13, 2013.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio et al., Deterministically encoding quantum information using 100-photon schrödinger cat states, Science, vol.342, issue.6158, pp.607-610, 2013.

J. Koch, V. E. Manucharyan, M. H. Devoret, and L. Glazman, Charging effects in the inductively shunted Josephson junction, Phys. Rev. Lett, vol.103, p.217004, 2009.

J. Braumülcer, M. Sandberg, M. R. Vissers, A. Schneider, S. Schlör et al., Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment, Appl. Phys. Lett, vol.108, p.32601, 2016.

S. Richer, N. Maleeva, S. T. Skacel, I. M. Pop, and D. Divincenzo, Inductively shunted transmon qubit with tunable transverse and longitudinal coupling, Phys. Rev. B, vol.96, p.174520, 2017.

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. Van-der-wal et al., Josephson persistent-current qubit, Science, vol.285, issue.5430, pp.1036-1039, 1999.

V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single cooper-pair circuit free of charge offsets, Science, vol.326, issue.5949, pp.113-116, 2009.

N. E. Frattini, U. Vool, S. Shankar, A. Narla, K. M. Sliwa et al., 3-wave mixing josephson dipole element, Applied Physics Letters, vol.110, issue.22, p.222603, 2017.

J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source python framework for the dynamics of open quantum systems, Computer Physics Communications, vol.183, issue.8, pp.1760-1772, 2012.

J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A python framework for the dynamics of open quantum systems, Computer Physics Communications, vol.184, issue.4, pp.1234-1240, 2013.

T. Oliphant, NumPy: A guide to NumPy, 2006.

E. Jones, T. Oliphant, and P. Peterson, SciPy: Open source scientific tools for Python, 2001.

S. Behnel, R. Bradshaw, C. Citro, L. Dalcin, D. S. Seljebotn et al., The best of both worlds. Computing in Science Engineering, vol.13, pp.31-39, 2011.

J. D. Hunter, Matplotlib: A 2d graphics environment, Computing In Science & Engineering, vol.9, issue.3, pp.90-95, 2007.

N. Roch, E. Flurin, F. Nguyen, P. Morfin, P. Campagne-ibarcq et al., Widely tunable, nondegenerate three-wave mixing microwave device operating near the quantum limit, Physical Review Letters, vol.108, issue.14, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00700677