  Two-Ievel (qubit) clock systems are often used to perform precise measurement
of time. In this work, we propose a compression protocol for $n$ identically
prepared states of qubit clocks. The protocol faithfully encodes the states
into $(1/2)\log n$ qubits and $(1/2)\log n$ classical bits and works even in
the presence of noise. If the purity of the clock states is fixed, $(1/2)\log
n$ qubits are sufficient. We also prove that this protocol requires the minimum
amount of total memory among all protocols with vanishing error in the large
$n$ limit.
