  We observe experimentally the harmonic oscillations of a macroscopic
many-body wavefunction of the bosonic condensate of exciton-polaritons confined
in an elliptical trap. The oscillations are caused by quantum beats between two
size-quantized states of the polariton condensate split in energy due to the
ellipticity of the trap. The eigen-functions of these states are $p$-shape
orbitals tilted with respect to the main and the short axes of the trap. The
beats between these states manifest themselves in a macroscopic periodical
redistribution of the polariton density in real space. The control of
frequency, amplitude and phase of the beats is achieved by sending non-resonant
laser pulses to specific spots inside the trap. We visualize the condensate
wave-function dynamics on a streak-camera and map them to the Bloch sphere
demonstrating the implementation of Hadamard and Pauli-Z operations. The decay
time of the observed oscillations is on a nanosecond scale. It exceeds the
individual exciton-polariton life-time by two orders of magnitude and the
coherence-time of the condensate by one order of magnitude.
