  We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier
transform, in a superconducting qutrit. The qutrit is encoded in the lowest
three energy levels of a capacitively shunted flux device, operated at the
optimal flux-symmetry point. We use an efficient decomposition of the
Walsh-Hadamard gate into two unitaries, generated by off-diagonal and diagonal
Hamiltonians respectively. The gate implementation utilizes simultaneous
driving of all three transitions between the three pairs of energy levels of
the qutrit, one of which is implemented with a two-photon process. The gate has
a duration of 35 ns and an average fidelity over a representative set of
states, including preparation and tomography errors, of 99.2%, characterized
with quantum state tomography. Compensation of ac-Stark and Bloch-Siegert
shifts is essential for reaching high gate fidelities.
