A superconducting phase-shift system comprising: an all-pass filter comprising at least one variable inductance element (110, 112) 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 (110, 112); 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 (110, 112) based on a characteristic of the phase-control current; wherein the at least one variable inductance element (110, 112) comprises: a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, (114, 118) coupled to one of an input and an output of the all-pass filter; and a second SQUID (116, 120) coupled to the first capacitor (C 2) interconnecting the second SQUID (116, 120) and the low-voltage rail, wherein the first SQUID (114, 118) and the second SQUID (116, 120) are connected in series via a conductive coupling, wherein the first SQUID (114, 118) and the second SQUID (116, 120) 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 (114, 118) and the second SQUID (116, 120) via an inductive coupling between each of the first SQUID (114, 118) and the second SQUID (116, 120) and the control line. an all-pass filter comprising at least one variable inductance element (110, 112) 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 (110, 112); 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 (110, 112) based on a characteristic of the phase-control current; wherein the at least one variable inductance element (110, 112) comprises: a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, (114, 118) coupled to one of an input and an output of the all-pass filter; and a second SQUID (116, 120) coupled to the first capacitor (C 2) interconnecting the second SQUID (116, 120) and the low-voltage rail, wherein the first SQUID (114, 118) and the second SQUID (116, 120) are connected in series via a conductive coupling, wherein the first SQUID (114, 118) and the second SQUID (116, 120) 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 (114, 118) and the second SQUID (116, 120) via an inductive coupling between each of the first SQUID (114, 118) and the second SQUID (116, 120) and the control line. a first Superconducting Quantum Interference Device, hereinafter referred to as SQUID, (114, 118) coupled to one of an input and an output of the all-pass filter; and a second SQUID (116, 120) coupled to the first capacitor (C 2) interconnecting the second SQUID (116, 120) and the low-voltage rail, wherein the first SQUID (114, 118) and the second SQUID (116, 120) are connected in series via a conductive coupling, wherein the first SQUID (114, 118) and the second SQUID (116, 120) 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 (114, 118) and the second SQUID (116, 120) via an inductive coupling between each of the first SQUID (114, 118) and the second SQUID (116, 120) and the control line.