On the Performance of Interleavers for Quantum Turbo Codes

Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Existing QTCs have been constructed using uniform random interleavers. However, interleaver design plays an important role in the optimization of classical turbo codes. Consequently, inspired by the widely used classical-to-quantum isomorphism, this paper studies the integration of classical interleaving design methods into the paradigm of quantum turbo coding. Simulations results demonstrate that error floors in QTCs can be lowered significantly, while decreasing memory consumption, by proper interleaving design without increasing the overall decoding complexity of the system

Decoherence and quantum error correction for quantum computing and communications.

Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. In this thesis, the nature of decoherence is studied and mathematically modelled; and QECCs are designed and optimized so that they exhibit better error correction capabilities.Las tecnologías cuánticas presentan un enorme potencial para resolver, de una forma eficiente, tareas de procesado de información tales como la factorización en números primos, la búsqueda en bases de datos no estructuradas o simulación de macromoléculas complejas. Como resultado de esta capacidad para resolver problemas que no se pueden tratar con medios clásicos, las máquinas cuánticas tienen el potencial de revolucionar el mundo moderno mediante aplicaciones como el diseño de fármacos, la optimización de procesos, las comunicaciones completamente seguras o el quantum machine learning. Sin embargo, la información cuántica tiende a sufrir errores producidos por la interacción denominada decoherencia cuántica. La decoherencia cuántica describe la pérdida de coherencia, y así de la información, de los estados cuánticos asociada a la inevitable interacción de estos con su entorno. Este efecto está presente en todas las tareas de procesado cuántico de la información, sea la transmisión, el procesado o el almacenamiento de la información cuántica. Como consecuencia, la protección de los estados cuánticos mediante los denominados códigos correctores de errores cuánticos es de vital importancia para poder construir ordenadores cuánticos que sean fiables. Entender los procesos físicos que constituyen la decoherencia cuántica y su modelado teórico es fundamental para poder construir métodos de corrección de errores cuánticos de forma eficiente. En esta tesis doctoral se abarcan el modelado matemático de la decoherencia cuántica; y el diseño y optimización de códigos correctores de errores para obtener mejores rendimientos en dicha tarea.Teknologia kuantikoak, konputazionalki konplexuak diren eta egungo teknologien bidez ebatzi ezin daitezkeen arazoei aurre egiteko aukera eskaintzen du. Adibidez, modu eraginkor batean zenbakiak beren osagai lehenetan faktorizatzeko, datu-base desegituratuetan bilaketak burutzeko edota makromolekula konplexuak simulatzeko aukera eskaintzen du. Ondorioz, konputazio kuantikoa gizartearen eta zientziaren aurrerapenean ezinbesteko tresna bilakatu daiteke. Besteak beste, botika diseinuan, finantza-krisien aurreikustean, konputagailu sareen segurtasuna sendotzean edo genomen sekuentziazioan aplikatu daiteke teknologia kuantikoa. Hala ere, egungo teknologiaren bitartez oraindik ezinezkoa da konputazio kuantikoak eskaini ditzaken aukera guztiak burutzeko gai den konputagailu kuantikoa eraikitzea. Informazio kuantikoak erroreak jasateko duen joerak sorturiko fidagarritasun falta da ezgaitasun horren kausa. Errore horiek, sistema kuantikoek euren ingurumenarekin dituzten interakzioen ondorio dira. Prozesu fisiko horien multzoari dekoherentzia deritzaio eta teknologia kuantikoen zeregin guztietan ageri da. Hortaz, informazio kuantikoa errore-zuzentze kodeen bidez babestea beharrezkoa da era zuzenean funtzionatzeko ahalmena duten konputagailu kuantikoak eraiki ahal izateko. Kode horiek modu eraginkor batean sortu ahal izateko, dekoherentzia prozesuak ulertzea eta matematikoki modelatzea funtsezkoa da. Tesi honetan dekoherentziaren modelatze matematikoa eta errore-zuzentze kode kuantikoen optimizazioa ikertu ditugu

Depolarizing Channel Mismatch and Estimation Protocols for Quantum Turbo Codes

Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Decoding for QTCs typically assumes that perfect knowledge about the channel is available at the decoder. However, in realistic systems, such information must be estimated, and thus, there exists a mismatch between the true channel information and the estimated one. In this article, we first heuristically study the sensitivity of QTCs to such mismatch. Then, existing estimation protocols for the depolarizing channel are presented and applied in an off-line manner to provide bounds on how the use of off-line estimation techniques affects the error correction capabilities of QTCs. Finally, we present an on-line estimation method for the depolarizing probability, which, different from off-line estimation techniques, neither requires extra qubits, nor increases the latency. The application of the proposed method results in a performance similar to that obtained with QTCs using perfect channel information, while requiring less stringent conditions on the variability of the channel than off-line estimation techniques

Decoherence and quantum error correction for quantum computing and communications.

Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. In this thesis, the nature of decoherence is studied and mathematically modelled; and QECCs are designed and optimized so that they exhibit better error correction capabilities.Las tecnologías cuánticas presentan un enorme potencial para resolver, de una forma eficiente, tareas de procesado de información tales como la factorización en números primos, la búsqueda en bases de datos no estructuradas o simulación de macromoléculas complejas. Como resultado de esta capacidad para resolver problemas que no se pueden tratar con medios clásicos, las máquinas cuánticas tienen el potencial de revolucionar el mundo moderno mediante aplicaciones como el diseño de fármacos, la optimización de procesos, las comunicaciones completamente seguras o el quantum machine learning. Sin embargo, la información cuántica tiende a sufrir errores producidos por la interacción denominada decoherencia cuántica. La decoherencia cuántica describe la pérdida de coherencia, y así de la información, de los estados cuánticos asociada a la inevitable interacción de estos con su entorno. Este efecto está presente en todas las tareas de procesado cuántico de la información, sea la transmisión, el procesado o el almacenamiento de la información cuántica. Como consecuencia, la protección de los estados cuánticos mediante los denominados códigos correctores de errores cuánticos es de vital importancia para poder construir ordenadores cuánticos que sean fiables. Entender los procesos físicos que constituyen la decoherencia cuántica y su modelado teórico es fundamental para poder construir métodos de corrección de errores cuánticos de forma eficiente. En esta tesis doctoral se abarcan el modelado matemático de la decoherencia cuántica; y el diseño y optimización de códigos correctores de errores para obtener mejores rendimientos en dicha tarea.Teknologia kuantikoak, konputazionalki konplexuak diren eta egungo teknologien bidez ebatzi ezin daitezkeen arazoei aurre egiteko aukera eskaintzen du. Adibidez, modu eraginkor batean zenbakiak beren osagai lehenetan faktorizatzeko, datu-base desegituratuetan bilaketak burutzeko edota makromolekula konplexuak simulatzeko aukera eskaintzen du. Ondorioz, konputazio kuantikoa gizartearen eta zientziaren aurrerapenean ezinbesteko tresna bilakatu daiteke. Besteak beste, botika diseinuan, finantza-krisien aurreikustean, konputagailu sareen segurtasuna sendotzean edo genomen sekuentziazioan aplikatu daiteke teknologia kuantikoa. Hala ere, egungo teknologiaren bitartez oraindik ezinezkoa da konputazio kuantikoak eskaini ditzaken aukera guztiak burutzeko gai den konputagailu kuantikoa eraikitzea. Informazio kuantikoak erroreak jasateko duen joerak sorturiko fidagarritasun falta da ezgaitasun horren kausa. Errore horiek, sistema kuantikoek euren ingurumenarekin dituzten interakzioen ondorio dira. Prozesu fisiko horien multzoari dekoherentzia deritzaio eta teknologia kuantikoen zeregin guztietan ageri da. Hortaz, informazio kuantikoa errore-zuzentze kodeen bidez babestea beharrezkoa da era zuzenean funtzionatzeko ahalmena duten konputagailu kuantikoak eraiki ahal izateko. Kode horiek modu eraginkor batean sortu ahal izateko, dekoherentzia prozesuak ulertzea eta matematikoki modelatzea funtsezkoa da. Tesi honetan dekoherentziaren modelatze matematikoa eta errore-zuzentze kode kuantikoen optimizazioa ikertu ditugu

Approximating decoherence processes for the design and simulation of quantum error correction codes on classical computers

Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this article, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer

Approximating decoherence processes for the design and simulation of quantum error correction codes on classical computers

Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this article, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer