Quantum Error Correction

1 / 11

Quantum Error Correction - PowerPoint PPT Presentation

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.

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

PowerPoint Slideshow about 'Quantum Error Correction' - yardley

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

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

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

Bits with errors

Correct information

Quantum Error Correction
• Then we get (assuming )
Quantum Error Correction
• Then we get (assuming )
Quantum Error Correction
• Then we get (assuming )
Quantum Error Correction
• More generally, if the error effected on the system in state is of the form
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
• 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 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 Correction
• Notice that if lives in a Hilbert space of dimension then the operators

Form a basis for the set of possible operation elements