# Numerical techniques for finding the distances of quantum codes

@article{Dumer2014NumericalTF, title={Numerical techniques for finding the distances of quantum codes}, author={Ilya Dumer and Alexey A. Kovalev and Leonid P. Pryadko}, journal={2014 IEEE International Symposium on Information Theory}, year={2014}, pages={1086-1090} }

We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces complexity exponent of all existing deterministic techniques designed for codes with small relative distances (which include all known families of quantum LDPC codes), and also surpasses the probabilistic technique for sufficiently high code rates.

## 6 Citations

Distance verification for LDPC codes

- Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

This work re-designs the existing generic algorithms of distance verification and derives their complexity for LDPC codes and obtains new complexity bounds with provable performance expressed in terms of the erasure-correcting thresholds of longLDPC codes.

Thresholds for Correcting Errors, Erasures, and Faulty Syndrome Measurements in Degenerate Quantum Codes.

- Computer SciencePhysical review letters
- 2015

This work gives explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum low-density parity-check codes with logarithmic or larger distances that are parametrically better than the existing analytical bound based on percolation.

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

- Computer SciencePhysical Review A
- 2018

Analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes are studied, with a simple model of independent X and Z errors.

Lattice Codes with Built in Dynamical Protection for Solid State Quantum Computation

- Computer Science
- 2014

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any oenalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank

- MathematicsJournal of Mathematical Physics
- 2019

We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other after freezing $k$…

Homology-changing percolation transitions on finite graphs

- MathematicsJournal of Mathematical Physics
- 2022

We consider homological edge percolation on a sequence $(\mathcal{G}_t)_t$ of finite graphs covered by an infinite (quasi)transitive graph $\mathcal{H}$, and weakly convergent to $\mathcal{H}$.…

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