quantum error correction
Download
Skip this Video
Download Presentation
Quantum Error Correction

Loading in 2 Seconds...

play fullscreen
1 / 11

Quantum Error Correction - PowerPoint PPT Presentation


  • 120 Views
  • Uploaded on

Quantum Error Correction. Michele Mosca . Quantum Error Correction: Bit Flip Errors . Suppose the environment will effect error (i.e. operation ) on our quantum computer when the environment is in state.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Quantum Error Correction' - yardley


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
quantum error correction bit flip errors
Quantum Error Correction: Bit Flip Errors
  • Suppose the environment will effect error

(i.e. operation )

on our quantum computer when the environment is in state

analysis of 6 qubit system which uses syndrome bits to correct errors
Analysis of 6-qubit system which uses syndrome bits to correct errors
  • Then we get (assuming )

Bits with errors

Correct information

quantum error correction1
Quantum Error Correction
  • Then we get (assuming )
quantum error correction2
Quantum Error Correction
  • Then we get (assuming )
quantum error correction3
Quantum Error Correction
  • Then we get (assuming )
quantum error correction4
Quantum Error Correction
  • More generally, if the error effected on the system in state is of the form
quantum error correction5
Quantum Error Correction
  • and if the state only consists of mixtures of superpositions of codewords and

(that is, )

then the correction procedure (call it ) will map

main error correction theorem
Main Error Correction Theorem
  • Theorem 10.2: Suppose C is a quantum code and is the error-correction operation constructed in the proof of Theorem 10.1 to recover from a noise process with operation elements . Suppose is a quantum operation with elements which are linear combinations of the . Then the error correction operation also corrects the effects of the noise process on the code C.
quantum error correction6
Quantum Error Correction
  • E.g. the error correction procedure that we have described for the 3-qubit code will correct any combination of error operators
quantum error correction7
Quantum Error Correction
  • Notice that if lives in a Hilbert space of dimension then the operators

Form a basis for the set of possible operation elements

ad