Logical operator tradeoff for local quantum codes

Details Logical operator tradeoff for local quantum codes Logical operator tradeoff for local quantum codes

2010-11-15

arxiv.org/abs/1011.3529v2

Physics

Quantum Physics

17 pages, 1 figure. (v2): improved proofs of Theorems 5 and 6, other minor changes

Scientific paper

We study the structure of logical operators in local D-dimensional quantum codes, considering both subsystem codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors. We show that if the code distance is d, then any logical operator can be supported on a set of specified geometry containing \tilde d qubits, where \tilde d d^{1/(D-1)} = O(n) and n is the code length. Our results place limitations on partially self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that grow with system size. We also show that two-dimensional codes defined by local commuting projectors admit logical "string" operators and are not self correcting.

Affiliated with

Also associated with

No associations

Rating

Logical operator tradeoff for local quantum codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Logical operator tradeoff for local quantum codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Logical operator tradeoff for local quantum codes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-463065