Pauli Channel Online Estimation Protocol for Quantum Turbo Codes

Martinez, Josu Etxezarreta; Fuentes, Patricio; Crespo, Pedro M.; Garcia-Frías, Javier

doi:10.1109/qce49297.2020.00023

Cited by 4 publications

(20 citation statements)

References 16 publications

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“…Let us now consider the toric codes with d ∈ {7, 9} 12 and the QTC from ref. 11 designed for the depolarizing channel. These error correction codes are capable of operating at a word error rate (WER) of WER ≈ {5 × 10 −3 , 10 −3 , 10 −6 }, respectively, for p = 0.05 (see "Methods" for definition of WER and description of QECC numerical simulations), while for for p = 0.15 they fail completely, resulting in WER ≈ 1.…”

Section: Discussionmentioning

confidence: 99%

“…Lor j ðω; tÞ þ Nðω; tÞ; (11) where N(ω, t) denotes the white Gaussian process and Lor j (ω, t), j = 1, 2 represents the two Gaussian random processes with Lorentzian PSD. Table 1 shows the values obtained for the parameters of the noise processes in Eq.…”

Section: Modeling Of T 1 and Tmentioning

confidence: 99%

“…12 ) and the QTC of rate 1/9 in (ref. 11 ) have been carried out, in order to estimate their performance for the different scenarios that have been studied. Toric codes belong to the more general family of surface codes 38 and are [[2d 2 , 2, d]] QECCs defined by the grid length of the code d. A blocklength of k = 1000 logical qubits has been selected for the QTC, as in refs.…”

Section: Qecc Numerical Simulationmentioning

confidence: 99%

“…In consequence, the quantum information community has gone to extraordinary lengths to construct QECCs that are capable of efficiently reversing the deleterious effects that quantum information experiences due to the interaction between qubits and their surrounding environment. This has led to the design of several promising families of QECCs, such as quantum Reed-Muller codes 1 , quantum low-density parity-check (QLDPC) codes 2 , quantum low-density generator matrix codes [3][4][5] , quantum convolutional codes 6 , quantum turbo codes (QTCs) [7][8][9][10][11] , and quantum topological codes 12,13 . It is important to point out that the aforementioned QECCs are utilized in the context of conventional qubit-based quantum computation, in which the physical elements are realized by discrete two-level systems.…”

Section: Introductionmentioning

confidence: 99%

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Time-varying quantum channel models for superconducting qubits

et al. 2021

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The decoherence effects experienced by the qubits of a quantum processor are generally characterized using the amplitude damping time (T1) and the dephasing time (T2). Quantum channel models that exist at the time of writing assume that these parameters are fixed and invariant. However, recent experimental studies have shown that they exhibit a time-varying (TV) behaviour. These time-dependant fluctuations of T1 and T2, which become even more pronounced in the case of superconducting qubits, imply that conventional static quantum channel models do not capture the noise dynamics experienced by realistic qubits with sufficient precision. In this article, we study how the fluctuations of T1 and T2 can be included in quantum channel models. We propose the idea of time-varying quantum channel (TVQC) models, and we show how they provide a more realistic portrayal of decoherence effects than static models in some instances. We also discuss the divergence that exists between TVQCs and their static counterparts by means of a metric known as the diamond norm. In many circumstances this divergence can be significant, which indicates that the time-dependent nature of decoherence must be considered, in order to construct models that capture the real nature of quantum devices.

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Section: Discussionmentioning

confidence: 99%

Section: Modeling Of T 1 and Tmentioning

confidence: 99%

Section: Qecc Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time-varying quantum channel models for superconducting qubits

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“…Content may change prior to final publication. [92] and in the quantum paradigm [29], [93]- [96]. Given that matters pertaining to channel parameter estimation are outside of the scope of this paper, we will also assume that the probability distribution of the channel is known to the receiver.…”

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Degeneracy and Its Impact on the Decoding of Sparse Quantum Codes

et al. 2021

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Approach for the construction of non-Calderbank-Steane-Shor low-density-generator-matrix–based quantum codes

et al. 2020

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The game took me to Saint Andrew's College and so we now turn to that marvelous place. I would not be who I am today had I not spent two years at SAC. True to its motto, the place molded me into a significantly more mature individual and taught me skills that have shined with brilliance during my time as a PhD student. To all my teachers, coaches, and friends at SAC, thank you. Special shoutouts to my friends in 1st Hockey and the so-called "Dawgz": Graham, Humza, David, YoungWoo, West, and Andy. Although we have not seen each other in a long time, I know our friendship still runs as deep as it did when we gamed away our days at the Manor. Following this theme of childhood friends, thank you to Isma, Guille, Luken, and Andrey. From the day we first met in kindergarten at Saint Patrick's, our passion for sports and later on fitness kept us united. I pray that our games of pádel never stop being so competitive.Barring chance or extremely good fortune, those I will thank next will likely never read this dissertation. Thank you to R. A Salvatore, Steven Erikson, Brandon Sanderson, Patrick Rothfuss, and all those other authors from whom I have learned so much. Thank you also to Satoshi Nakamoto. I do not doubt that your creation will change the world for the better. I must also thank the Counting Crows, Rise Against, Machine Gun Kelly, and the Chainsmokers for motivating me in all those instances when my discipline evaporated. In relation to this, I must also thank the people at Youtube and Nespresso (and Iñigo Gutierrez by association); procrastination via the classic video and black coffee combo will never get old. Finally, a special shoutout to all those online meetings, home workouts, and quarantine periods brought to me by the COVID-19 pandemic. Somehow, throughout this entire ordeal, my work has not been impeded at any point in time. I have been extremely fortunate.Having left the best for last, I must now turn to those closest to my heart. After spending days thinking about how to thank my parents appropriately, I found it best to use the following quote by the writer Chuck Palahniuk: "First your parents, they give you your life, but then they try to give you their life". Despite this, I am still left with a feeling of insufficiency. I guess my parents have done so much for me that it is not possible to put my gratitude into words. Gracias attatto y amatxo por todo. The same goes for my sister Idoia, to whom I owe more than can be expressed. Thank you for always being there, for always having time to talk, and most of all, for always being willing to listen. Through thick and thin, your presence has never failed to remind me that there is always light at the end of the tunnel. Lastly, thank you Moose for being such an energetic furball and for greeting me at the door everyday as if you had not seen me in years.Alas, it is now time for me to thank one final person. Maria, you, above anyone else, have lived through the highs and the lows of my PhD. You have seen the extent to which manuscript revisions can frustr...

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Pauli Channel Online Estimation Protocol for Quantum Turbo Codes

Cited by 4 publications

References 16 publications

Time-varying quantum channel models for superconducting qubits

Time-varying quantum channel models for superconducting qubits

Degeneracy and Its Impact on the Decoding of Sparse Quantum Codes

Approach for the construction of non-Calderbank-Steane-Shor low-density-generator-matrix–based quantum codes

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