  Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear
equations with $N$ variables and condition number $\kappa$ can be solved on a
quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially
faster than any classical algorithms, its improvements and applications have
been extensively investigated. The state-of-the-art quantum algorithm for this
problem is due to Costa, An, Sanders, Su, Babbush, and Berry (2022), with
optimal query complexity $\Theta(\kappa)$. An important question left is
whether parallelism can bring further optimization. In this paper, we study the
limitation of parallel quantum computing on this problem. We show that any
quantum algorithm for solving systems of linear equations with time complexity
$\operatorname{poly}(\log(N), \kappa)$ has a lower bound of $\Omega(\kappa)$ on
the depth of queries, which is tight up to a constant factor.
