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 (30)
- Good Quantum Error-Correcting Codes Exist
- Topological quantum memory
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- A Theory of Fault-Tolerant Quantum Computation
- Stabilizer Codes and Quantum Error Correction
- Topological Quantum Distillation
- Simple Quantum Error Correcting Codes
- Sparse Graph Codes for Quantum Error-Correction
- Overhead and noise threshold of fault-tolerant quantum error correction
- Capacities of Quantum Erasure Channels
- Fault-Tolerant Error Correction with Efficient Quantum Codes
- Active stabilisation, quantum computation and quantum state synthesis
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Tradeoffs for reliable quantum information storage in 2D systems
- Efficient fault-tolerant quantum computing
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Classification of topologically protected gates for local stabilizer codes
- Error Threshold for Color Codes and Random 3-Body Ising Models
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Quantum "hyperbicycle" low-density parity check codes with finite rate
- Fault-tolerant logical gates in quantum error-correcting codes
- Fault-tolerant quantum computing with color codes
- A Proposed Quantum Low Density Parity Check Code
- Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
- Subsystem codes with spatially local generators
- Improved quantum hypergraph-product LDPC codes
- Fault-Tolerant Logical Gate Networks for CSS Codes
- Scalable Quantum Computation in the Presence of Large Detected-Error Rates
- New constructions of CSS codes obtained by moving to higher alphabets
- Homological Product Codes
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