arXiv subjects

Eren Guttentag

Publications and source records attributed to Eren Guttentag.

2 recordsLinked to original sources

arXiv2026

Fault-Tolerant QLDPC Syndrome Measurement via LDGM Encoding

We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM codes with column and row weights that result in measured stabilizers that have constant weight, thus preserving the desirable properties of the underlying QLDPC code. This process allows for control over stabilizer weights and SM code distance, resulting in significantly better performance than repeated syndrome extraction and allowing for both higher distances and fewer syndrome measurements. We implement these SM codes on a distance-5 rotated surface code, and show that this procedure results in a lower probability of logical error. As syndrome measurements performed are a reasonable metric for the time a circuit takes to implement, we conclude that these LDGM codes allow for improved implementation of QLDPC codes without sacrificing the low weights of the syndrome measurements performed.

quant-ph↗

arXiv2023

Robust Syndrome Extraction via BCH Encoding

Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS code is to choose a syndrome measurement code, a classical block code that encodes the syndrome of the underlying quantum code by defining additional stabilizer measurements. We propose the use of primitive narrow-sense BCH codes as syndrome measurement codes. We show that these codes asymptotically require $O(t\log\ell)$ extra measurements, where $\ell$ is the number of stabilizer generators of the quantum code and $t$ is the number of errors corrected by the BCH code. Previously, the best known general method of constructing QDS codes out of quantum codes requires $O(t^3\log\ell)$ extra measurements. As the number of additional syndrome measurements is a reasonable metric for the amount of additional time a general QDS code requires, we conclude that our construction protects against the same number of syndrome errors with significantly less time overhead.

quant-ph↗