  Quantum bits (qubits) are prone to several types of errors due to
uncontrolled interactions with their environment. Common strategies to correct
these errors are based on architectures of qubits involving daunting hardware
overheads. A hopeful path forward is to build qubits that are inherently
protected against certain types of errors, so that the overhead required to
correct remaining ones is significantly reduced. However, the foreseen benefit
rests on a severe condition: quantum manipulations of the qubit must not break
the protection that has been so carefully engineered. A recent qubit - the
cat-qubit - is encoded in the manifold of metastable states of a quantum
dynamical system, thereby acquiring continuous and autonomous protection
against bit-flips. Here, in a superconducting circuit experiment, we implement
a cat-qubit with bit-flip times exceeding 10 seconds. This is a four order of
magnitude improvement over previous cat-qubit implementations. We prepare and
image quantum superposition states, and measure phase-flip times above 490
nanoseconds. Most importantly, we control the phase of these quantum
superpositions without breaking bit-flip protection. This experiment
demonstrates the compatibility of quantum control and inherent bit-flip
protection at an unprecedented level, showing the viability of these dynamical
qubits for future quantum technologies.
