• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

204 submissions , 162 unreviewed
5,024 questions , 2,178 unanswered
5,345 answers , 22,686 comments
1,470 users with positive rep
815 active unimported users
More ...

  Dimensions of quantum cell automata's state space

+ 1 like - 0 dislike

In the paper

C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573

about quantum dots, it is stated that the basis vectors in the state space for a single cell (four quantum dots) are of the form
|\phi_1\rangle =  |\begin{array}{cccc}0&0&0&1 \\ 0&0&0&1\end{array}\rangle \\
\vdots \\
|\phi_{16}\rangle =  |\begin{array}{cccc}1&0&0&0 \\ 1&0&0&0\end{array}\rangle
where the columns are related to the dot in which there is an electron, and the rows tell the projection of the spin (first row meaning that the spin points upwards). Therefore, the authors state that there are $16$ different basis states and that the dimension of the state space for $N$ cells is $16^N$.

However, I don't see why they only take into account states in which the electrons have opposite spin projections, and they are ignoring basis states like
|\begin{array}{cccc}1&1&0&0 \\ 0&0&0&0\end{array}\rangle
Of course, because of the exclusion principle, the unique possibility for having two electrons in the same dot is that they have opposite spins, like in state $|\phi_1\rangle$, but I don't see why there should be such a restriction for two electrons being in different dots. If we take into account these extra basis states, the dimension of the state space for a single cell would be
\dfrac{8!}{2! \cdot 6!} = 28\ ,
so we have $28^N$ for $N$ cells.

Why aren't these states taken into account?

asked Jul 7, 2022 in General Physics by SrJaimito (5 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights