A superconducting phase-shift system comprising: an all-pass filter comprising at least one variable inductance element and a first capacitor (C 2 ) connected to a low-voltage rail, the all-pass filter being configured to receive an input signal and to provide an output signal that is phase-shifted relative to the input signal based on a variable inductance provided by each of the at least one variable inductance element ; and a phase controller configured to provide a phase-control current (I PH ) onto a control line to control the variable inductance of the at least one variable inductance element based on a characteristic of the phase-control current; wherein the at least one variable inductance element comprises: a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, coupled to one of an input and an output of the all-pass filter ; and a second SQUID coupled to the first capacitor (C 2 ) interconnecting the second SQUID and the low-voltage rail, wherein the first SQUID and the second SQUID are connected in series via a conductive coupling, wherein the first SQUID and the second SQUID provide the variable inductance in each of the at least one variable inductance element; wherein the phase control current controls a variable inductance of the first SQUID and the second SQUID via an inductive coupling between each of the first SQUID and the second SQUID and the control line . an all-pass filter comprising at least one variable inductance element and a first capacitor (C 2 ) connected to a low-voltage rail, the all-pass filter being configured to receive an input signal and to provide an output signal that is phase-shifted relative to the input signal based on a variable inductance provided by each of the at least one variable inductance element ; and a phase controller configured to provide a phase-control current (I PH ) onto a control line to control the variable inductance of the at least one variable inductance element based on a characteristic of the phase-control current; wherein the at least one variable inductance element comprises: a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, coupled to one of an input and an output of the all-pass filter ; and a second SQUID coupled to the first capacitor (C 2 ) interconnecting the second SQUID and the low-voltage rail, wherein the first SQUID and the second SQUID are connected in series via a conductive coupling, wherein the first SQUID and the second SQUID provide the variable inductance in each of the at least one variable inductance element; wherein the phase control current controls a variable inductance of the first SQUID and the second SQUID via an inductive coupling between each of the first SQUID and the second SQUID and the control line . a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, coupled to one of an input and an output of the all-pass filter ; and a second SQUID coupled to the first capacitor (C 2 ) interconnecting the second SQUID and the low-voltage rail, wherein the first SQUID and the second SQUID are connected in series via a conductive coupling, wherein the first SQUID and the second SQUID provide the variable inductance in each of the at least one variable inductance element; wherein the phase control current controls a variable inductance of the first SQUID and the second SQUID via an inductive coupling between each of the first SQUID and the second SQUID and the control line . <EOS>