I don’t know whether you think that it’s possible to understand quantum computing at some level without understanding quantum mechanics first, the theory of everything that quantum computing is based on. If one thinks that it’s not possible to understand QC properly without a decent understanding of QM then that means big trouble.
There are several problems with QM that makes it difficult to get your head round it. The first is the philosophy behind QM. QM was developed in a flurry of activity in the mid-to-late 1920s, a time of incredible results achieved at bewildering pace. But even a hundred years later philosophers and physicists concerned with the philosophy of QM are still struggling.
The second problem with QM is that it is
highly mathematical; The Hungarian physicist John von Neumann made the definitive mathematical description of QM (QM for mathematicians, if you like) and this features some scary aspects: infinite-dimensional
vectors (i.e. arrays, ordered lists or tuples) and each element in the vector (‘list’) is a
complex number. Dealing with
infinite-length lists / tuples / infinite-dimensional vectors is horrible, and although physicists and electronics engineers may deal with complex numbers as part of some equation that will ultimately give you real-valued answers (ie ordinary numbers), they are not used to dealing with physical quantities that are end results and are complex-valued. This is because complex numbers make no sense when used for physical quantities. In QM, complex numbers can’t be avoided, in fact their presence is a basic controlling aspect of the theory.
Thirdly, to proceed to more advanced QM it is necessary to have a full understanding of
special relativity. Without this, it’s not possible to get to a description of elementary particles. This brings in a load more physics as a pre-requisite.
There are a number of other problematic topics that I could list that come in when dealing with later developments in QM, but these are beyond that which is needed for a firm foundation in QM.
