  The role of entanglement is discussed in the Harrow-Hassidim-Lloyd (HHL)
algorithm. We compute all tripartite entanglement at every steps of the HHL
algorithm. The tripartite entanglement is generated in the first quantum phase
estimation (QPE) step. However, it turns out that amount of the generated
entanglement is not maximal except very rare cases. In the second rotation step
some tripartite entanglement is annihilated. Thus, the net tripartite
entanglement is diminished. At the final inverse-QPE step the matrix inversion
task is completed at the price of complete annihilation of the entanglement. An
implication of this result is discussed.
