Binary classical information is routinely encoded in the two metastable
states of a dynamical system. Since these states may exhibit macroscopic
lifetimes, the encoded information inherits a strong protection against
bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of
metastable states of a quantum dynamical system, thereby acquiring bit-flip
protection. An outstanding challenge is to gain quantum control over such a
system without breaking its protection. If this challenge is met, significant
shortcuts in hardware overhead are forecast for quantum computing. In this
experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds.
This is a four order of magnitude improvement over previous cat-qubit
implementations, and six orders of magnitude enhancement over the single photon
lifetime that compose this dynamical qubit. This was achieved by introducing a
quantum tomography protocol that does not break bit-flip protection. We prepare
and image quantum superposition states, and measure phase-flip times above 490
nanoseconds. Most importantly, we control the phase of these superpositions
while maintaining the bit-flip time above ten seconds. This work demonstrates
quantum operations that preserve macroscopic bit-flip times, a necessary step
to scale these dynamical qubits into fully protected hardware-efficient
architectures