Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes
arXiv:1412.6172 · doi:10.1103/PhysRevLett.115.050502
Abstract
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum LDPC codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.
10 pages, 2 figures
References in corpus (9)
- Topological Quantum Distillation
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Error Threshold for Color Codes and Random 3-Body Ising Models
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Fault-tolerant logical gates in quantum error-correcting codes
- Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
- Scalable Quantum Computation in the Presence of Large Detected-Error Rates
- New constructions of CSS codes obtained by moving to higher alphabets
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