  Encoding quantum information into superpositions of multiple Fock states of a
harmonic oscillator can provide protection against errors, but it comes with
the cost of requiring more complex quantum gates that need to address multiple
Fock states simultaneously. Therefore, characterizing the quantum process
fidelity of these gates also becomes more challenging. Here, we demonstrate the
use of coherent-state quantum process tomography (csQPT) for a bosonic-mode
superconducting circuit. CsQPT uses coherent states as input probes for the
quantum process in order to completely characterize the quantum operation for
an arbitrary input state. We show results for this method by characterizing a
logical quantum gate constructed using displacement and SNAP operations on an
encoded qubit. With csQPT, we are able to reconstruct the Kraus operators for
the larger Hilbert space rather than being limited to the logical subspace.
This allows for a more accurate determination of the different error mechanisms
that lead to the gate infidelity.
