A parametric amplifier system (10; 50) comprising: an input/output, I/O, transmission line (12; 52) to propagate a signal tone; and an impedance matching network coupled to the I/O transmission line, the impedance matching network comprising a plurality of impedance matching elements (54, 56, 58) each configured to provide a respective frequency pole associated with the signal tone, each of the plurality of impedance matching elements comprising a resonator configured as an inductor (L P2, L P3) and a capacitor (C P2, C P3) arranged in parallel, and each of the plurality of impedance matching elements being interconnected via a capacitor (C 12, C 23), wherein one of the plurality of impedance matching elements comprises a non-linearity circuit (16; 64; 100) configured to amplify the signal tone and arranged in parallel with a capacitor (CP 1) between a capacitive coupling to another of the plurality of impedance matching elements and a low-voltage rail; wherein the non-linearity circuit (16; 64; 100) comprises first and second arrays of radio frequency, RF, superconducting quantum interference devices, SQUIDs,, the first and second arrays being arranged in parallel and each comprising a plurality of RF SQUIDs arranged between a first terminal and a second terminal of the non-linearity circuit to form an inductive path of the signal tone, each RF SQUID comprising a Josephson junction (Jx) and a pair of inductors (L X1, L X2) arranged in parallel with the Josephson junction, wherein an inductor of the pair of inductors of each RF SQUID of the plurality of RF SQUIDs is common to a preceding RF SQUID of the plurality of RF SQUIDs; wherein the non-linearity circuit further comprises a transformer configured to inductively couple a pump current (I PUMP) to the at least one inductive path of the signal tone; and wherein the impedance matching network is configured to provide impedance matching of the signal tone between the I/O transmission line and the non-linearity circuit. an input/output, I/O, transmission line (12; 52) to propagate a signal tone; and an impedance matching network coupled to the I/O transmission line, the impedance matching network comprising a plurality of impedance matching elements (54, 56, 58) each configured to provide a respective frequency pole associated with the signal tone, each of the plurality of impedance matching elements comprising a resonator configured as an inductor (L P2, L P3) and a capacitor (C P2, C P3) arranged in parallel, and each of the plurality of impedance matching elements being interconnected via a capacitor (C 12, C 23), wherein one of the plurality of impedance matching elements comprises a non-linearity circuit (16; 64; 100) configured to amplify the signal tone and arranged in parallel with a capacitor (CP 1) between a capacitive coupling to another of the plurality of impedance matching elements and a low-voltage rail; wherein the non-linearity circuit (16; 64; 100) comprises first and second arrays of radio frequency, RF, superconducting quantum interference devices, SQUIDs,, the first and second arrays being arranged in parallel and each comprising a plurality of RF SQUIDs arranged between a first terminal and a second terminal of the non-linearity circuit to form an inductive path of the signal tone, each RF SQUID comprising a Josephson junction (Jx) and a pair of inductors (L X1, L X2) arranged in parallel with the Josephson junction, wherein an inductor of the pair of inductors of each RF SQUID of the plurality of RF SQUIDs is common to a preceding RF SQUID of the plurality of RF SQUIDs; wherein the non-linearity circuit further comprises a transformer configured to inductively couple a pump current (I PUMP) to the at least one inductive path of the signal tone; and wherein the impedance matching network is configured to provide impedance matching of the signal tone between the I/O transmission line and the non-linearity circuit.