Coherent-state quantum process tomography of continuous-variable gates in superconducting circuits

Encoding quantum information into a collection of a harmonic oscillator's Fock states shows a promising alternative towards universal quantum computing. Superpositions of multiple Fock states provide protection against errors at the cost of more complex quantum gates that address multiple Fock states simultaneously. Therefore, characterizing these gates becomes also more challenging. Here, we perform coherent state quantum process tomography (cs-QPT) for a continuous-variable superconducting circuit. Cs-QPT uses coherent states as input probes for the quantum process to completely characterize the quantum operation for an arbitrary input state. We show the results of this method by characterizing a quantum gate consisting of displacement and arbitrary phase (SNAP) operations on an encoded logical qubit. With this method we reconstruct the quantum process matrix for a large Hilbert space rather than being limited to the logical subspace. This allows for a more accurate determination of the various error mechanisms that lead to infidelity, and therefore can help in the diagnosis of the performance of continuous-variable quantum gates.