Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits*

We provide an explicit construction of a universal gate set for continuous-variable quantum computation with microwave circuits. Such a universal set has been first proposed in quantum-optical setups, but its experimental implementation has remained elusive in that domain due to the difficulties in engineering strong nonlinearities. We show that a realistic three-wave mixing microwave architecture based on the superconducting nonlinear asymmetric inductive element [1] allows us to overcome this difficulty.
As an application, we show that this architecture allows for the generation of a cubic phase state with an experimentally feasible procedure. This work highlights a practical advantage of microwave circuits with respect to optical systems for the purpose of engineering non-Gaussian states and opens the quest for continuous-variable algorithms based on few repetitions of elementary gates from the continuous-variable universal set.
Ref. [1] Frattini et al., Appl. Phys. Lett. 110, 222603 (2017).