Systems and methods for reading out the states of superconducting flux qubits may couple magnetic flux representative of a qubit state to a DC-SQUID in a variable transformer circuit. The DC-SQUID is electrically coupled in parallel with a primary inductor such that a time-varying (e.g., AC) drive current is divided between the DC-SQUID and the primary inductor in a ratio that is dependent on the qubit state. The primary inductor is inductively coupled to a secondary inductor to provide a time-varying (e.g., AC) output signal indicative of the qubit state without causing the DC-SQUID to switch into a voltage state. Coupling between the superconducting flux qubit and the DC-SQUID may be mediated by a routing system including a plurality of latching qubits. Multiple superconducting flux qubits may be coupled to the same routing system so that a single variable transformer circuit may be used to measure the states of multiple qubits.