A circuit, comprising: a plurality of Josephson junctions (140a, 140b,... 140n) arranged in series in a loop; at least one magnetic element producing magnetic flux (Φ) through the loop; a plurality of superconducting resonators (130a, 130b,... 130n), each resonator coupled to the loop between a different neighboring pair of Josephson junctions of the plurality of Josephson junctions; a plurality of ports (110a, 110b,... 110n; 211, 212, 213), each port coupled to at least one of the plurality of resonators at ends of the resonators opposite to ends at which the resonators are coupled to the loop; and at least one controller coupled to the plurality of ports and configured to provide a plurality of pumping signals to the plurality of ports, the plurality of pumping signals comprising: a first pumping signal provided as an input to a first port of the plurality of ports and configured to off-resonantly pump a first resonant mode of the circuit, the first resonant mode having a resonant frequency ω a; a second pumping signal provided as an input to a second port of the plurality of ports and configured to off-resonantly pump a second resonant mode of the circuit, the second resonant mode having a resonant frequency ω b; and a third pumping signal provided as an input to a third port of the plurality of ports and configured to off-resonantly pump a third resonant mode of the circuit, the third resonant mode having a resonant frequency ω c, wherein the third resonant mode is a common mode of the first and second resonant modes, wherein the first pumping signal has a frequency | ω b - ω c |, wherein the second pumping signal has a frequency |ω c - ω a |, wherein the third pumping signal has a frequency |ω a - ω b |, wherein a phase of the first pumping signal plus a phase of the second pumping signal minus a phase of the third pumping signal is configured to be equal to an odd integer multiple of ±π/2, so that the plurality of pumping signals cause the circuit to function as a circulator between the plurality of ports. a plurality of Josephson junctions (140a, 140b,... 140n) arranged in series in a loop; at least one magnetic element producing magnetic flux (Φ) through the loop; a plurality of superconducting resonators (130a, 130b,... 130n), each resonator coupled to the loop between a different neighboring pair of Josephson junctions of the plurality of Josephson junctions; a plurality of ports (110a, 110b,... 110n; 211, 212, 213), each port coupled to at least one of the plurality of resonators at ends of the resonators opposite to ends at which the resonators are coupled to the loop; and at least one controller coupled to the plurality of ports and configured to provide a plurality of pumping signals to the plurality of ports, the plurality of pumping signals comprising: a first pumping signal provided as an input to a first port of the plurality of ports and configured to off-resonantly pump a first resonant mode of the circuit, the first resonant mode having a resonant frequency ω a; a second pumping signal provided as an input to a second port of the plurality of ports and configured to off-resonantly pump a second resonant mode of the circuit, the second resonant mode having a resonant frequency ω b; and a third pumping signal provided as an input to a third port of the plurality of ports and configured to off-resonantly pump a third resonant mode of the circuit, the third resonant mode having a resonant frequency ω c, wherein the third resonant mode is a common mode of the first and second resonant modes, a first pumping signal provided as an input to a first port of the plurality of ports and configured to off-resonantly pump a first resonant mode of the circuit, the first resonant mode having a resonant frequency ω a; a second pumping signal provided as an input to a second port of the plurality of ports and configured to off-resonantly pump a second resonant mode of the circuit, the second resonant mode having a resonant frequency ω b; and a third pumping signal provided as an input to a third port of the plurality of ports and configured to off-resonantly pump a third resonant mode of the circuit, the third resonant mode having a resonant frequency ω c, wherein the third resonant mode is a common mode of the first and second resonant modes, wherein the first pumping signal has a frequency | ω b - ω c |, wherein the second pumping signal has a frequency |ω c - ω a |, wherein the third pumping signal has a frequency |ω a - ω b |, wherein a phase of the first pumping signal plus a phase of the second pumping signal minus a phase of the third pumping signal is configured to be equal to an odd integer multiple of ±π/2, so that the plurality of pumping signals cause the circuit to function as a circulator between the plurality of ports.