  Huffman Compression, also known as Huffman Coding, is one of many compression
techniques in use today. The two important features of Huffman coding are
instantaneousness that is the codes can be interpreted as soon as they are
received and variable length that is a most frequent symbol has length smaller
than a less frequent symbol. The traditional Huffman coding has two procedures:
constructing a tree in O(n^2) and then traversing it in O(n). Quantum computing
is a promising approach of computation that is based on equations from Quantum
Mechanics. Instantaneousness and variable length features are difficult to
generalize to the quantum case. The quantum coding field is pioneered by
Schumacher works on block coding scheme. To encode N signals sequentially, it
requires O(N3) computational steps. The encoding and decoding processes are far
from instantaneous. Moreover, the lengths of all the codewords are the same. A
Huffman-coding-inspired scheme for the storage of quantum information takes
O(N(log N)a) computational steps for a sequential implementation on
non-parallel machines.
