Quantcast
  • 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.

News

PO is now at the Physics Department of Bielefeld University!

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

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Subgroups of the Clifford Group

+ 2 like - 0 dislike
1710 views

We recall the definition of a Clifford group (over $n$ qubits) is the set of unitary transformations:

$$\{U: UPU^\dagger\in\mathcal{P}\}$$

where $\mathcal{P}$ denotes the corresponding Pauli group (again over $n$ qubits).

What progress has been made in characterizing the subgroups of the Clifford group, and in particular, what progress has been made in characterizing those subgroups isomorphic to the Pauli Group?

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user ruadath
asked Jun 18, 2014 in Resources and References by ruadath (15 points) [ no revision ]
retagged Jun 19, 2014
Progress, from which starting point?

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user Niel de Beaudrap
Not sure what you mean.

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user ruadath
You ask what "progress" there has been made in (etc.), which implies that you are asking about what developments there has been from some starting point. What is it that you already know? Are you just asking whether there exists some characterization? Do you mind if there isn't a characterization, but a description of some subgroups of the Clifford group which are isomorphic to the Pauli group? Do you care if you get an answer which restricts to inner automorphisms of $\mathrm{GL}(2^n)$ or do you want a more complete theory? What base knowledge are you assuming when you say "progress"?

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user Niel de Beaudrap
I'm just asking if there is some characterization (I have no base knowledge, besides that obviously the Pauli group itself is a subgroup)

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user ruadath

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:
p$\hbar$ysicsOver$\varnothing$low
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).
Please complete the anti-spam verification




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

Your rights
...