Chapter 12 Approximation
About quantifying precision in implementations of quantum circuits using the notion of metrics — more specifically, the trace distance. Also about the practical feasibility of universal sets of gates and correctly distinguishing non-orthogonal states described by density operators.
We have talked a lot about preparing specific quantum states and constructing specific unitary operations, but the space of states of any quantum system is a continuous space, and the set of unitary transformations is also continuous.
It is entirely unrealistic to imagine that in the actual world we will be able to prepare, for example, a qubit precisely in the state