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Quantum Low-Density Parity Check Codes (qLDPC codes)

Quantum Low-Density Parity-Check Codes (qLDPC) are a class of quantum error-correc­ting codes designed to protect quantum infor­ma­tion from noise while using sparse constraints. Like their classi­cal LDPC counter­parts, qLDPC codes are defined by parity checks that involve only a small number of qubits, which is crucial for practi­cal imple­men­ta­tion on hardware with limited connec­ti­vity. Beyond measu­re­ment effici­ency, qLDPC codes are attrac­tive because they offer a path to overco­ming the overhead bottlen­ecks of more tradi­tio­nal codes, such as surface codes, whose distance (quantity that deter­mi­nes the number of errors that the code can correct) grows only with the linear size of the lattice. In contrast, qLDPC codes can, in princi­ple, achieve constant encoding rate (ratio between the number of logical and physi­cal qubits) while maintai­ning growing distance, drama­ti­cally reducing the number of physi­cal qubits requi­red per logical qubit.

Topics in the Subfield Quantum error correction:

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Surface codes

Surface codes are currently the leading archi­tec­ture for practi­cal quantum error correc­tion and are widely regarded as one of the most promi­sing approa­ches due to their…

Color codes

Color codes are topolo­gi­cal quantum error correc­tion codes that encode logical qubits within a two dimen­sio­nal lattice whose faces can be colored using three distinct colors. This struc­ture enables…

Cat Qubits

Cat qubits are quantum bits encoded in Schrö­din­ger cat states, that is, in super­po­si­ti­ons of two coher­ent states of a harmo­nic oscil­la­tor, typically micro­wave photons stored within a…

Self Correc­ting Quantum Codes

Self-correc­ting quantum codes passi­vely protect data via…

Perfect matching

Perfect matching decoding is an error correc­tion approach that is widely used in topolo­gi­cal quantum error correc­tion codes such as the Surface Code. The central idea is that…

Cluste­ring

In quantum error correc­tion, classi­cal decoders inter­pret error signa­tures (syndro­mes) to fix qubits. Cluste­ring is an…

ML based decoding in QEC

Quantum Error Correc­tion (QEC) genera­tes large amounts of so called syndrome data in order to identify which…

Magic Gate iIjection

Fault tolerant quantum compu­ters rely on quantum error correc­tion codes. However, these codes typically support only a limited…

Code switching

Code switching refers to the process of dynami­cally changing the error correc­tion code used to protect quantum infor­ma­tion, often in order to…

Lattice Surgery

Lattice surgery is a method for imple­men­ting logical gate opera­ti­ons between qubits encoded in topolo­gi­cal quantum error correc­tion codes, particularly…

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