Efficient and exact quantum compression

We present a divide and conquer based algorithm for optimal quantum compression/decompression, using O(n(log4n)log log n) elementary quantum operations. Our result provides the first quasi-linear time algorithm for asymptotically optimal (in size and fidelity) quantum compression and decompression. We also outline the quantum gate array model to bring about this compression in a quantum computer. Our method uses various classical algorithmic tools to significantly improve the bound from the previous best known bound of O(n3) for this operation.