Abstract
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly identify and correct errors as soon as they occur. We propose a linear-time maximum likelihood decoder for surface codes over the quantum erasure channel. This decoding algorithm for dealing with qubit loss is optimal both in terms of performance and speed.
Highlights
Surface codes are among the best candidates to ensure the fault tolerance of a quantum computer
We propose a linear-time maximum likelihood decoder for surface codes over the quantum erasure channel
We propose a linear-time maximum likelihood decoder for erasures over surface codes
Summary
Surface codes [1,2,3] are one of the leading candidates to ensure the fault tolerance of a quantum computer. The loss of a qubit is equivalent to applying a random Pauli error to this qubit, while giving, as additional data, the position of the error For stabilizer codes, this extra information reduces the decoding problem to solving a linear system, which can be done with cubic complexity. In the particular case of surface codes, the syndrome of an error is a set of vertices of a lattice and decoding amounts to finding a set of paths connecting these vertices by pairs or to the boundary. We propose a linear-time maximum likelihood decoder for erasures over surface codes. This is optimal both in terms of performance and in terms of complexity. We generalize the approach to surfaces with boundaries, more relevant for practical purposes [3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
