I have not yet figured out why different definitions for MakeBoxes
occur, but it seems that adding this definition in version 10 allows your specific example to parse and evaluate as desired:
Needs["Quantum`Computing`"]
Needs["Quantum`Notation`"]
SetComputingAliases[];
MakeExpression[
TagBox[SuperscriptBox[
RowBox[{"(",
TagBox[Quantum`Computing`Private`a_, zz020TPdat,
Quantum`Computing`Private`opts1___], ")"}],
RowBox[{AdjustmentBox["\[CircleTimes]", BoxBaselineShift -> -(3/4)],
TagBox[Quantum`Computing`Private`n_, zz020TPend,
Quantum`Computing`Private`opts2___]}]], zz020TP,
Quantum`Computing`Private`opts0___], Quantum`Computing`Private`form_] :=
MakeExpression[
RowBox[{"zz020TensorPower", "[", Quantum`Computing`Private`a, ",",
Quantum`Computing`Private`n, "]"}], Quantum`Computing`Private`form]
If you confirm that this solves your problem for the specific example I shall try to figure out why this definition is missing or different when the package is loaded in version 10. (I copied this from version 7, after loading the package.)