Correctable noise of Quantum Error Correcting Codes under adaptive concatenation

Abstract

We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are optimally adapted to use error syndrome information from the previous levels of the code. We use the Shannon entropy of these channels to estimate the thresholds of correctable noise for QECCs and find considerable improvements under this adaptive concatenation. Similar methods could be used to increase quantum fault tolerant thresholds.

5 pages, no figures, RevTex4, minor changes, similar to final publication version

References in corpus (6)

• Good Quantum Error-Correcting Codes Exist
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• New lower bounds on the non-zero capacity of Pauli Channels
• Exact Performance of Concatenated Quantum Codes
• Generalized Performance of Concatenated Quantum Codes -- A Dynamical Systems Approach
• An upper bound on quantum fault tolerant thresholds

Cited by in corpus (12)

• Entanglement-assisted quantum turbo codes
• New lower bounds on the non-zero capacity of Pauli Channels
• Errors and pseudo-thresholds for incoherent and coherent noise
• Hard decoding algorithm for optimizing thresholds under general Markovian noise
• Entropic singularities give rise to quantum transmission
• Cluster-based architecture for fault-tolerant quantum computation
• Detecting positive quantum capacities of quantum channels
• Error rates and resource overheads of encoded three-qubit gates
• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
• Facets of correlated non-Markovian channels
• Allowing leakage can increase quantum transmission
• An upper bound on quantum fault tolerant thresholds