Strong resilience of topological codes to depolarization

By H. Bombin, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber, Miguel Angel Martin-Delgado. 2012

170 citations recorded by the source corpus.

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase via both large-scale Monte Carlo simulations and the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this result agrees within error bars with the result for a different class of codes—topological color codes—where the mapping yields interesting new types of interacting eight-vertex models.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f5646e039ba0d57127ea8e3b8087bdf5fde2ada1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits (2012, background): “With recent advances in quantum information processing technologies (e.g. [5], [6], [8], [24]) and improvements to fault-tolerant thresholds (e.g. [4], [12], [13]), larger quantum devices are becoming increasingly attainable; as the complexity and size of these devices grow, hand optimizations will…”
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning (2013, background): “Given the high cost of the fault tolerant implementations of the T gate [1, 14], exceeding the cost of Clifford group gates by as much as a factor of a hundred or more, it has recently been proposed that efficient circuits should minimize the number of T gates, and more specifically the number of T…”
Single-Shot Fault-Tolerant Quantum Error Correction (2014, background): “It is maybe also due to their strong physical flavor that topological stabilizer codes display other very interesting features, such as the fact that classical processing for error correction is often efficient [15,31], that error thresholds are high [15,32], and that computations can be performed i”
Quantum memories at finite temperature (2014, background): “Moreover, the study of decoding has foundations in the study of glassy statistical mechanical models (Andrist et al., 2014; Bombin et al., 2012; Dennis et al., 2002; Wang et al., 2003).”
Quantum error correction for quantum memories (2013, unknown): “9% in the numerical study by Bombin et al. (2012).”