  Lloyd has considered the ultimate limitations physics places on quantum
computers. He concludes in particular that for an ``ultimate laptop'' (a
computer of one liter of volume and one kilogram of mass) the maximum number of
operations per second is bounded by $10^{51}$. The limit is derived considering
ordinary quantum mechanics. Here we consider additional limits that are placed
by quantum gravity ideas, namely the use of a relational notion of time and
fundamental gravitational limits that exist on time measurements. We then
particularize for the case of an ultimate laptop and show that the maximum
number of operations is further constrained to $10^{47}$ per second.
