We report the parametric amplification of a microwave signal in a Kerr medium formed from superconducting qubits. Two mutually coupled flux qubits, embedded in the current antinode of a superconducting coplanar waveguide resonator, are used as a nonlinear element. Shared Josephson junctions provide the qubit-resonator coupling, resulting in a device with a measured gain of about 20 dB. We argue, that this arrangement represents a unit cell which can be straightforwardly extended to a quasi one-dimensional quantum metamaterial with a large tunable Kerr nonlinearity.New developments in circuit quantum electrodynamics has resulted in the possibility of signal detection close to and even below the standard quantum limit. This work was motivated by microwave quantum engineering, 1-3 including quantum information processing devices. 4,5 The sensitivity of cryogenic semiconductor amplifiers with reasonable power consumption in both the MHz 6 and GHz (commercially available) range are all currently above the quantum limit. At very low temperatures it is quite natural to use the parametric effect for amplification which adds no additional noise to the signal. In practice, a nonlinear superconducting oscillator can be used for this purpose. 7,8 In this case, usually a nonlinearity of superconducting weak links 9,10 is exploited. Very recently the squeezing of quantum noise and its measurement below the standard quantum limit was demonstrated. 11 These successful experiments have motivated the development of new parametric amplifiers based on Josephson junctions, 12,13 DC squids, 13-15 high kinetic inductance of weak links, 16 or disordered superconductors. 17 Superconducting qubits also exhibit a strong nonlinearity 18 and therefore are good candidates for parameteric amplification. 19 In this paper, we demonstrate parametric amplification exploiting the nonlinearity of a pair of superconducting flux qubits coupled to a coplanar waveguide resonator. These qubits represent a unit cell which can be easily extended to a one-dimensional array. Such an array can be considered as a medium with large Kerr nonlinearity. Neglecting the interactions between the modes, a nonlinear oscillator can be described by the Hamiltonian 20where is the reduced Planck constant, a and a † are the creation and the annihilation operators, ω n is the angular frequency of the n-th mode of the oscillator, and K n is the Kerr constant, which is a measure of the nonlinearity in the system. The qubits contribute to the nonlinear inductance of the resonator per unit length according tõ Then, the Kerr constant can be calculated by 20where u n (x) = 2 Lrl sin( nπx l ), l is the length of the resonator,L r the linear inductance of the resonator per unit length, I r the current flowing in the resonator, I cqr the critical current of the Josephson junction shared by the resonator and qubit, andL i are the Taylor coefficients characterizing the nonlinearity of the inductance. The Kerr constant can be determined for every nonlinear medium. In optics, the Kerr c...