Optimal Bacon-Shor codes

Abstract

We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming independent noise, we find the optimal block size in terms of the bit-flip error probability p_X and the phase error probability p_Z, and determine how the probability of a logical error depends on p_X and p_Z. We show that a single Bacon-Shor code block, used by itself without concatenation, can provide very effective protection against logical errors if the noise is highly biased (p_Z / p_X >> 1) and the physical error rate p_Z is a few percent or below. We also derive an upper bound on the logical error rate for the case where the syndrome data is noisy.

arXiv comment21 pages, 6 figures

References in corpus (5)

• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Stabilizer Formalism for Operator Quantum Error Correction
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Subsystem fault tolerance with the Bacon-Shor code
• Fault-tolerant quantum computation against biased noise

Cited by in corpus (1)

• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction