Systems and methods are provided for reading an associated state of a qubit. A first soliton is injected along a first Josephson transmission line coupled to the qubit. A velocity of the first soliton is selected according to a physical length of the qubit and a characteristic frequency of the qubit. A second soliton is injected at the selected velocity along a second Josephson transmission line that is not coupled to the qubit. A delay associated with the first soliton is determined relative to the second soliton.