Honestly, a lot of the terminology you used is beyond my comprehension, either due to not being part of that niche community of science, or because I just don't know enough science -- or both! When I next go on a posting binge and am doing a lot of leisure reading, I'm going to cross-reference your post with google to try and learn some stuff... then I'll respond to you. Might be a while though?

no problem. do feel free to ask (and anyone else too). when you start an internet discussion you never know who you're really discussing yet.

if it is helpful i can try to compile a glossary- would be useful to know which terms to add though.

i'll define a couple of the terms i used as a start:

**Transport** - something physically moving from A to B

**Quantum walk - **a mode of transport that is the quantum mechanical analogue of the classical random walk. It has discrete and continuous time flavours, discrete is useful for algorithms and continuous is useful for modelling physical phenomena

**Hilbert space** - a vector space with an L2 (Euclidean) norm. i don't know how to put this in English but its where quantum mechanical states live. elements of this vector space (i.e. specific quantum states) can have a mixture of real and imaginary components.

**BQP - **bounded error quantum polynomial time- the complexity class of problems that can be solved with bounded error (so the computer may make a mistake, but you'll know how often its likely to be wrong) in polynomial time, so as your problem size increases, the time taken to solve it increases according to a polynomial function like x^2.... or x^100000000000000 which would still be pretty slow. if we can prove where this lies in comparison to the complexity classes for classical algorithms, we will be able to prove whether quantum computers are genuinely fast or our algorithms for classical computers are just really inefficient. so yes, an entire subject area exists for computers that we don't know for sure are better than the ones we already have, what's more, we don't even know if we can build them in real life!!!

**Decoherence - **the process by which a quantum mechanical (coherent, von Neumann entropy = 0- technical, don't worry, included for completeness) state evolves into a classical (decoherent, von Neumann entropy > 0) state. This occurs when the quantum mechanical system interacts with another system (quantum or classical) but only arises if you continue to model the system in its original reference frame (technical term is basis but that's probably not very illuminating), rather than expanding to consider both the system+thing its interacting with. this is important when considering the potential relevance of quantum mechanics to biology because heat and surrounding particles cause decoherence, so the question is, whether anything interesting can happen before then.

**Everett's many world interpretation - **an interpretation of quantum mechanics that takes the mathematical formalism at face value. This solves the problem of the 'collapse of the wavefunction' by positing that every possible state in fact arises, and evolves in a 'parallel universe' that becomes causally separated from the other possible states represented in the wavefunction upon decoherence, which is when, traditionally, the wave function is considered to collapse and the system take on a classical, definite, state.

any more for any more?

i have sacrificed some clarity in an effort to be concise and may well have garbled something but if anything is incomprehensible please ask