• 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.


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


(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 ...

  Properties of controlled z-rotations

+ 1 like - 0 dislike

Given n qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which will change this gate into one that preserves phase when flipping all the qubits. That is |1111..1> will have the same phase as |000..0> ans so on.

An example would be c-z. All input states remain unchanged except |11>, which picks up a - sign. However, if you put an S gate on each qubit (a pi/2 phase gate) you will find that |00> and |11> are left unchanged, and |01> and |10> pick up an i. That is, each basis state has the same quantum amplitude after the gate as its bitwise flipped counterpart.

I haven't proven this, but I have tested it for 2, 3 and 4 qubits. However I haven't been able to do the same thing for gates with more than one control qubit, such as c-c-z. Is anyone aware of any reason why this might be, or any even slightly relevant research which might shed light on this?

Btw, if it helps, the reason I ask is that I am looking at using a coherent optical state to mediate entangling interactions between qubits. A coherent state is defined by a complex number, and in this particular system, when it interacts with a qubit, this complex number can be displaced in an arbitrary direction conditional on the state of the qubit, |0> and |1> displace the coherent state in opposite directions. When you use a series of these controlled displacements to take the coherent state in a closed path in the complex plane, this leaves a a phase on the qubits of the form e^(±iA) where A is the area enclosed by the path, and the sign is dependant on whether the path is travelling clockwise or anti-clockwise. You can use this effect to build entangling gates, specifically c-not as shown in http://arxiv.org/abs/quant-ph/0509202.

I have been trying to describe a c-c-z gate using fewer qubit-bus interactions than building it out of many 2-qubit gates.

The types of paths I am looking at (if not all paths in general) all seem to have this property where flipping all the qubits does not affect the phase, but it seems not all multiqubit gates have this property (including c-c-z), but I haven't worked out a way of determining which do and which don't apart from trial and error.

Any help would be appreciated.

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Leo Rogers
asked Feb 27, 2015 in Theoretical Physics by Leo Rogers (5 points) [ no revision ]
Might TheoreticalComputerScience.SE be a better place for this?

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Jimdalf the Grey
Possibly, I guess its the kind of thing that could be physics, maths or CS. I guess I'll leave it here for the moment and if no one answers I'll have a look at the CS stackexchange.

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Leo Rogers
Can you describe more precisely what exactly is the property you want after the local unitaries are applied? Do you mean c-c-c-z in the first line rather than c-z-z-z?

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Māris Ozols
I mean c-z-z-z, i guess as a short hand for meaning multiple c-z's, so the first qubit is the only control qubit, and all the others are targets.

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Leo Rogers
I'll edit the main post to ad an example.

This post imported from StackExchange Physics at 2015-03-01 12:42 (UTC), posted by SE-user Leo Rogers

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).
Please complete the anti-spam verification

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

Your rights