A method of operating an apparatus, the apparatus comprising a first resonant cavity having a plurality of coherent quantum states, the first resonant cavity being coupled to a second resonant cavity via a Josephson junction, the method comprising: providing an input photon signal to the second resonant cavity that stimulates photon conversion from the first resonant cavity to the second resonant cavity and photon conversion from the second resonant cavity to the first resonant cavity, and that causes net dissipation of photons to be output from the second resonant cavity, wherein the input photon signal includes at least two photon signal components having different frequencies and each having an amplitude and a phase, wherein a first component of the input photon signal has a first frequency and a second component of the input photon signal has a second frequency, and wherein a difference between the first frequency and the second frequency is equal to a resonant frequency of the first resonant cavity; and adiabatically varying the amplitude and the phase of the at least two photon signal components of the input photon signal to cause a change in one or more of the plurality of coherent quantum states of the first resonant cavity, wherein adiabatically varying the amplitude and the phase of the at least two photon signal components of the input photon signal is performed such that each of the amplitude and the phase of each of the at least two photon signal components of the input photon signal has the same initial and final value before and after the adiabatically varying so as to result in a holonomic operation that produces said change in the one or more of the plurality of coherent quantum states of the first resonant cavity. providing an input photon signal to the second resonant cavity that stimulates photon conversion from the first resonant cavity to the second resonant cavity and photon conversion from the second resonant cavity to the first resonant cavity, and that causes net dissipation of photons to be output from the second resonant cavity, wherein the input photon signal includes at least two photon signal components having different frequencies and each having an amplitude and a phase, wherein a first component of the input photon signal has a first frequency and a second component of the input photon signal has a second frequency, and wherein a difference between the first frequency and the second frequency is equal to a resonant frequency of the first resonant cavity; and adiabatically varying the amplitude and the phase of the at least two photon signal components of the input photon signal to cause a change in one or more of the plurality of coherent quantum states of the first resonant cavity, wherein adiabatically varying the amplitude and the phase of the at least two photon signal components of the input photon signal is performed such that each of the amplitude and the phase of each of the at least two photon signal components of the input photon signal has the same initial and final value before and after the adiabatically varying so as to result in a holonomic operation that produces said change in the one or more of the plurality of coherent quantum states of the first resonant cavity.