We report on the design and implementation of a Field Programmable Josephson Amplifier (FPJA) - a compact and lossless superconducting circuit that can be programmed textit{in situ} by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work we demonstrate four modes of operation: frequency conversion ($-0.5~mathrm{dB}$ transmission, $-30~mathrm{dB}$ reflection), circulation ($-0.5~mathrm{dB}$ transmission, $-30~mathrm{dB}$ reflection, $30~mathrm{dB}$ isolation), phase-preserving amplification (gain $>20~mathrm{dB}$, $1~mathrm{photon}$ of added noise) and directional phase-preserving amplification ($-10~mathrm{dB}$ reflection, $18~mathrm{dB}$ forward gain, $8~mathrm{dB}$ reverse isolation, $1~mathrm{photon}$ of added noise). The system exhibits quantitative agreement with theoretical prediction. Based on a gradiometric Superconducting Quantum Interference Device (SQUID) with Nb/Al-AlO$_x$/Nb Josephson junctions, the FPJA is first-order insensitive to flux noise and can be operated without magnetic shielding at low temperature. Due to its flexible design and compatibility with existing superconducting fabrication techniques, the FPJA offers a straightforward route toward on-chip integration with superconducting quantum circuits such as qubits or microwave optomechanical systems.
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