Creation of superposition of arbitrary states encoded in two three-dimensional cavities

The principle of superposition is a key ingredient for quantum mechanics. A recent work (M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)) has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we propose a probabilistic approach for creating a superposition state of two arbitrary states encoded in two three-dimensional cavities. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of two coherent states is feasible with current circuit QED technology. Our method also works for other physical systems such as other types of superconducting qubits, natural atoms, quantum dots, and nitrogen-vacancy (NV) centers.