Application
Quantum Error Correction and Artificial Intelligence algorithms
Mathematical Principles of Information and Communications (MATHπCOM)
Group Description:
The Mathematical Principles of Information and Communications (MATHπCOM) group at Tecnun focuses its research on:
- Methods to achieve reliable quantum computing, including quantum noise modeling, quantum error correction, and quantum error mitigation.
- Communication and Information Theory, both classical and quantum, particularly in the design of advanced algorithms for information compression, storage, transmission, and processing.
- Digital and Analog Communication Networks and future Quantum Communication Systems.
- Statistical Signal Processing and System Optimization.
The group’s main objectives are to generate new knowledge in the mentioned fields and apply it in various sectors such as telecommunications, industry, mobility, and health. Notably, their research in error-correcting codes is fundamental for future quantum computers.
The scientific interest of the University of Navarra is to contribute to solving the challenges posed by society in collaboration with other individuals and institutions, with sustainable development and care for people and the environment as references for project orientation.
Researchers Pedro Crespo Bofill, Xabier Insausti Sarasola, and Josu Etxezarreta Martínez specialize, among other topics, in studying error correction in quantum algorithms and circuits (e.g., some of their recent works on quantum communication channels published in npj Quantum Information 7 (1), 1-10, 2021).
The group is composed of Josu Etxezarreta Martinez, Reza Dastbasteh, Antonio de Martí i Olius, Javier Oliva del Moral, Olatz Sanz, Xabier Insausti Sarasola, and Bruno Sunsundegi.
Activity description:
This activity focuses on quantum algorithms for error correction, a fundamental component in the development of scalable quantum computing. The problem will be addressed from the perspective of its relationship with artificial intelligence.
- Design and implement an error correction code capable of combining the available physical qubits in the quantum computer so that some of them remain protected and, possibly, can be used for computing tasks.
- Characterize decoherence processes to create a noise model as realistic as possible and adapted to the architecture where the error codes will be implemented.
- Explore how the decoding task of the code can be improved with AI and how improvements in the correction algorithms themselves can be transferred to comparable problems in AI.
Results
Dastbasteh, R.; Padashnick, F.; Crespo, P.; Grassl, M.; Sharafi, J.
Equivalence of constacyclic codes with shift constants of different orders Journal Article
In: Designs, Codes and Cryptography, 2025.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Equivalence of constacyclic codes with shift constants of different orders},
author = {Dastbasteh, R. and Padashnick, F. and Crespo, P. and Grassl, M. and Sharafi, J.
},
url = {https://link.springer.com/article/10.1007/s10623-024-01512-9},
doi = {doi.org/10.48550/arXiv.2403.04600},
year = {2025},
date = {2025-10-18},
journal = {Designs, Codes and Cryptography},
abstract = {Let a and b be two non-zero elements of a finite field F_q, where q > 2. It has been shown that if a and b have the same multiplicative order in F_q, then the families of a-constacyclic and b-constacyclic codes over F_q are monomially equivalent. In this paper, we investigate the monomial equivalence of a-constacyclic and b-constacyclic codes when a and b have distinct multiplicative orders. We present novel conditions for establishing monomial equivalence in such constacyclic codes, surpassing previous methods of determining monomially equivalent constacyclic and cyclic codes. As an application, we use these results to search for new linear codes more systematically. In particular, we present more than 70 new record-breaking linear codes over various finite fields, as well as new binary quantum codes.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
Let a and b be two non-zero elements of a finite field F_q, where q > 2. It has been shown that if a and b have the same multiplicative order in F_q, then the families of a-constacyclic and b-constacyclic codes over F_q are monomially equivalent. In this paper, we investigate the monomial equivalence of a-constacyclic and b-constacyclic codes when a and b have distinct multiplicative orders. We present novel conditions for establishing monomial equivalence in such constacyclic codes, surpassing previous methods of determining monomially equivalent constacyclic and cyclic codes. As an application, we use these results to search for new linear codes more systematically. In particular, we present more than 70 new record-breaking linear codes over various finite fields, as well as new binary quantum codes.
Berardini, E.; Dastbasteh, R.; Etxezarreta Martinez, J.; Jain, S.; Sanz Larrarte, O.
Asymptotically good CSS-T codes and a new construction of triorthogonal codes Journal Article
In: IEEE Journal on Selected Areas in Information Theory, 2025.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Asymptotically good CSS-T codes and a new construction of triorthogonal codes},
author = {Berardini, E. and Dastbasteh, R. and Etxezarreta Martinez, J. and Jain, S. and Sanz Larrarte, O. },
url = {https://arxiv.org/abs/2412.08586},
doi = {10.1109/JSAIT.2025.3582156},
year = {2025},
date = {2025-06-20},
journal = {IEEE Journal on Selected Areas in Information Theory},
abstract = {We propose a new systematic construction of CSS-T codes from any given CSS code using a map ϕ. When ϕ is the identity map I, we retrieve the construction of hu2021mitigating and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction (ϕ=I), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in jain2024. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
We propose a new systematic construction of CSS-T codes from any given CSS code using a map ϕ. When ϕ is the identity map I, we retrieve the construction of hu2021mitigating and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction (ϕ=I), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in jain2024. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.
Etxezarreta Martinez, J.; Schnabl, P.; Oliva del Moral, P.; Dastbasteh, R.; Crespo, P. M.; Otxoa, R. M.
Leveraging biased noise for more efficient quantum error correction at the circuit-level with two-level qubits Working paper
2025.
Abstract | Links | BibTeX | Tags: TECNUN
@workingpaper{nokey,
title = {Leveraging biased noise for more efficient quantum error correction at the circuit-level with two-level qubits},
author = {Etxezarreta Martinez, J. and Schnabl, P. and Oliva del Moral, P. and Dastbasteh, R. and Crespo, P.M. and Otxoa, R.M.},
url = {https://arxiv.org/abs/2505.17718},
doi = {doi.org/10.48550/arXiv.2505.17718},
year = {2025},
date = {2025-05-23},
abstract = {Tailoring quantum error correction codes (QECC) to biased noise has demonstrated significant benefits. However, most of the prior research on this topic has focused on code capacity noise models. Furthermore, a no-go theorem prevents the construction of CNOT gates for two-level qubits in a bias preserving manner which may, in principle, imply that noise bias cannot be leveraged in such systems. In this work, we show that a residual bias up to η ∼5 can be maintained in CNOT gates under certain conditions. Moreover, we employ controlled-phase (CZ) gates in syndrome extraction circuits and show how to natively implement these in a bias-preserving manner for a broad class of qubit platforms. This motivates the introduction of what we call a hybrid biased-depolarizing (HBD) circuit-level noise model which captures these features. We numerically study the performance of the XZZX surface code and observe that bias-preserving CZ gates are critical for leveraging biased noise. Accounting for the residual bias present in the CNOT gates, we observe an increase in the code threshold up to a 1.27% physical error rate, representing a 90% improvement. Additionally,
we find that the required qubit footprint can be reduced by up to a 75% at relevant physical error rates.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {workingpaper}
}
Tailoring quantum error correction codes (QECC) to biased noise has demonstrated significant benefits. However, most of the prior research on this topic has focused on code capacity noise models. Furthermore, a no-go theorem prevents the construction of CNOT gates for two-level qubits in a bias preserving manner which may, in principle, imply that noise bias cannot be leveraged in such systems. In this work, we show that a residual bias up to η ∼5 can be maintained in CNOT gates under certain conditions. Moreover, we employ controlled-phase (CZ) gates in syndrome extraction circuits and show how to natively implement these in a bias-preserving manner for a broad class of qubit platforms. This motivates the introduction of what we call a hybrid biased-depolarizing (HBD) circuit-level noise model which captures these features. We numerically study the performance of the XZZX surface code and observe that bias-preserving CZ gates are critical for leveraging biased noise. Accounting for the residual bias present in the CNOT gates, we observe an increase in the code threshold up to a 1.27% physical error rate, representing a 90% improvement. Additionally,
we find that the required qubit footprint can be reduced by up to a 75% at relevant physical error rates.
we find that the required qubit footprint can be reduced by up to a 75% at relevant physical error rates.
Dastbasteh, R.; Sanz Larrarte, O.; J. deMarti iOlius Etxezarreta Martinez, A.; Oliva del Moral, J.; Crespo Bofill, P.
Quantum CSS Duadic and Triadic Codes: New Insights and Properties Journal Article
In: Lecture Notes in Computer Science, vol. 15 176, 2025.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Quantum CSS Duadic and Triadic Codes: New Insights and Properties},
author = {Dastbasteh, R. and Sanz Larrarte, O. and Etxezarreta Martinez, J. deMarti iOlius, A. and Oliva del Moral, J. and Crespo Bofill, P. },
url = {https://link.springer.com/chapter/10.1007/978-3-031-81824-0_5},
doi = { https://doi.org/10.48550/arXiv.2407.07753},
year = {2025},
date = {2025-02-28},
urldate = {2025-02-28},
journal = {Lecture Notes in Computer Science},
volume = {15 176},
abstract = {In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes. Furthermore, we present a technique for computing or bounding the minimum distances of quantum codes constructed through this approach. Additionally, we introduce quantum CSS triadic codes, a family of quantum codes with a rate of at least 1/3.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes. Furthermore, we present a technique for computing or bounding the minimum distances of quantum codes constructed through this approach. Additionally, we introduce quantum CSS triadic codes, a family of quantum codes with a rate of at least 1/3.
deMarti iOlius, A.; Fuentes, P.; Orús, R.; Crespo, P.; Etxezarreta Martinez, J.
Decoding algorithms for surface codes Journal Article
In: Quantum, vol. 8, pp. 1498, 2024, ISBN: 2521-327X.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Decoding algorithms for surface codes},
author = {deMarti iOlius, A. and Fuentes, P. and Orús, R. and Crespo, P. and Etxezarreta Martinez, J. },
url = {https://quantum-journal.org/papers/q-2024-10-10-1498/pdf/},
doi = {doi.org/10.22331/q-2024-10-10-1498},
isbn = {2521-327X},
year = {2024},
date = {2024-10-10},
journal = {Quantum},
volume = {8},
pages = {1498},
abstract = {Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.
deMarti iOlius, A.; Etxezarreta Martinez, I.; Roffe, J.; Etxezarreta Martinez, J.
An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise Working paper
2024.
Abstract | Links | BibTeX | Tags: TECNUN
@workingpaper{nokey,
title = {An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise},
author = {deMarti iOlius, A. and Etxezarreta Martinez, I. and Roffe, J. and Etxezarreta Martinez, J. },
url = {https://arxiv.org/abs/2409.01440},
doi = {doi.org/10.48550/arXiv.2409.01440 Focus to learn more},
year = {2024},
date = {2024-09-02},
urldate = {2024-09-02},
abstract = {Fault-tolerant quantum computers must be designed in conjunction with classical co-processors that decode quantum error correction measurement information in real-time. In this work, we introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. The OTF post-processing stage removes qubits from the decoding graph until it has a tree-like structure. Provided that the resultant loop-free OTF graph supports a subset of qubits that can generate the syndrome, BP decoding is then guaranteed to converge. To enhance performance under circuit-level noise, we introduce a technique for sparsifying detector error models. This method uses a transfer matrix to map soft information from the full detector graph to the sparsified graph, preserving critical error propagation information from the syndrome extraction circuit. Our BP+OTF implementation first applies standard BP to the full detector graph, followed by BP+OTF post-processing on the sparsified graph. Numerical simulations show that the BP+OTF decoder achieves logical error suppression within an order of magnitude of state-of-the-art inversion-based decoders while maintaining almost-linear runtime complexity across all stages.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {workingpaper}
}
Fault-tolerant quantum computers must be designed in conjunction with classical co-processors that decode quantum error correction measurement information in real-time. In this work, we introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. The OTF post-processing stage removes qubits from the decoding graph until it has a tree-like structure. Provided that the resultant loop-free OTF graph supports a subset of qubits that can generate the syndrome, BP decoding is then guaranteed to converge. To enhance performance under circuit-level noise, we introduce a technique for sparsifying detector error models. This method uses a transfer matrix to map soft information from the full detector graph to the sparsified graph, preserving critical error propagation information from the syndrome extraction circuit. Our BP+OTF implementation first applies standard BP to the full detector graph, followed by BP+OTF post-processing on the sparsified graph. Numerical simulations show that the BP+OTF decoder achieves logical error suppression within an order of magnitude of state-of-the-art inversion-based decoders while maintaining almost-linear runtime complexity across all stages.
Dastbasteh, R.; Etxezarreta Martinez, J.; A. deMarti iOlius Nemec, A. Crespo Bofill.
An Infinite class of quantum codes derived from duadic constacyclic codes Working paper
Preprint, 2024.
Abstract | Links | BibTeX | Tags: TECNUN
@workingpaper{nokey,
title = {An Infinite class of quantum codes derived from duadic constacyclic codes},
author = {Dastbasteh, R. and Etxezarreta Martinez, J. and Nemec, A. deMarti iOlius, A. Crespo Bofill.},
url = {https://link.springer.com/article/10.1007/s11128-025-04828-0},
doi = {doi.org/10.48550/arXiv.2312.06504},
year = {2024},
date = {2024-05-27},
urldate = {2024-05-27},
abstract = {We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over F4. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family.},
howpublished = {Preprint},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {workingpaper}
}
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over F4. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family.
deMarti iOlius, A.; Etxezarreta Martinez, J.
The closed-branch decoder for quantum LDPC codes Working paper
2024.
Abstract | Links | BibTeX | Tags: TECNUN
@workingpaper{nokey,
title = {The closed-branch decoder for quantum LDPC codes},
author = {deMarti iOlius, A. and Etxezarreta Martinez, J.},
url = {https://arxiv.org/pdf/2402.01532},
doi = {doi.org/10.48550/arXiv.2402.01532},
year = {2024},
date = {2024-02-14},
urldate = {2024-02-14},
abstract = {Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. In this work, we present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case complexity loosely upper bounded by O(nmaxgrmaxbr), where maxgr and maxbr are tunable parameters that pose the accuracy versus speed trade-off of decoding algorithms. For the best precision, the maxgrmaxbr product increases exponentially as ∝djd, where d indicates the distance of the code and j indicates the average row weight of its parity check matrix. Nevertheless, we numerically show that considering small values that are polynomials of the code distance are enough for good error correction performance. The decoder is described to great extent and compared with the Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data qubit, phenomenological and circuit-level noise models for the class of Bivariate Bicycle (BB) codes. The results showcase a promising performance of the decoder, obtaining similar results with much lower complexity than BPOSD when considering the smallest distance codes, but experiencing some logical error probability degradation for the larger ones. Ultimately, the performance and complexity of the decoder depends on the product maxgrmaxbr, which can be considered taking into account benefiting one of the two aspects at the expense of the other.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {workingpaper}
}
Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. In this work, we present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case complexity loosely upper bounded by O(nmaxgrmaxbr), where maxgr and maxbr are tunable parameters that pose the accuracy versus speed trade-off of decoding algorithms. For the best precision, the maxgrmaxbr product increases exponentially as ∝djd, where d indicates the distance of the code and j indicates the average row weight of its parity check matrix. Nevertheless, we numerically show that considering small values that are polynomials of the code distance are enough for good error correction performance. The decoder is described to great extent and compared with the Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data qubit, phenomenological and circuit-level noise models for the class of Bivariate Bicycle (BB) codes. The results showcase a promising performance of the decoder, obtaining similar results with much lower complexity than BPOSD when considering the smallest distance codes, but experiencing some logical error probability degradation for the larger ones. Ultimately, the performance and complexity of the decoder depends on the product maxgrmaxbr, which can be considered taking into account benefiting one of the two aspects at the expense of the other.
Etxezarreta Martinez, J.; deMarti iOlius, A.; Crespo, P. M.
Superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels Journal Article
In: Physical Review A, vol. 108, iss. 3, 2023.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels},
author = {Etxezarreta Martinez, J. and deMarti iOlius, A. and Crespo, P. M. },
url = {https://quantumspain-project.es/wp-content/uploads/2023/10/2301.10132-2.pdf},
doi = {doi.org/10.48550/arXiv.2301.10132},
year = {2023},
date = {2023-09-12},
urldate = {2023-09-12},
journal = {Physical Review A},
volume = {108},
issue = {3},
abstract = {Quantum channel capacity is a fundamental quantity in order to understand how well quantum information can be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an unbounded number of channel uses. This leads to the phenomenon known as superadditivity, which refers to the fact that the regularized coherent information of n channel uses exceeds one-shot coherent information. In this article, we study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the considered systems. We make use of an argument based on the no-cloning bound in order to prove that the possible superadditive effects decrease as a function of the dimension for such family of channels. In addition, we prove that the capacity of the qudit depolarizing channel coincides with the coherent information when d→∞. We also discuss the private classical capacity and obtain similar results. We conclude that when high-dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate, but essentially the maximum possible rate for any quantum block code.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
Quantum channel capacity is a fundamental quantity in order to understand how well quantum information can be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an unbounded number of channel uses. This leads to the phenomenon known as superadditivity, which refers to the fact that the regularized coherent information of n channel uses exceeds one-shot coherent information. In this article, we study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the considered systems. We make use of an argument based on the no-cloning bound in order to prove that the possible superadditive effects decrease as a function of the dimension for such family of channels. In addition, we prove that the capacity of the qudit depolarizing channel coincides with the coherent information when d→∞. We also discuss the private classical capacity and obtain similar results. We conclude that when high-dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate, but essentially the maximum possible rate for any quantum block code.
De Marti i Olius, A.; Etxezarreta Martinez, J.; Fuentes, P.; Crespo, P. M.
Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding Journal Article
In: Physical Review A, vol. 108, iss. 2, 2023, ISBN: 2469-9934.
Abstract | Links | BibTeX | Tags: TECNUN
@article{,
title = {Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding},
author = {De Marti i Olius, A. and Etxezarreta Martinez, J. and Fuentes, P. and Crespo, P. M.},
url = {https://quantumspain-project.es/wp-content/uploads/2023/10/2212.11632.pdf},
doi = {doi.org/10.1103/PhysRevA.108.022401},
isbn = {2469-9934},
year = {2023},
date = {2023-08-03},
urldate = {2023-08-03},
journal = {Physical Review A},
volume = {108},
issue = {2},
abstract = {The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or nonidentical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the nonuniformities, and the relationship between X, Y, and Z errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an 18% improvement in the probability threshold pth under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent nonidentically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of 105.5% over the conventional MWPM strategy, and in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or nonidentical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the nonuniformities, and the relationship between X, Y, and Z errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an 18% improvement in the probability threshold pth under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent nonidentically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of 105.5% over the conventional MWPM strategy, and in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.
Etxezarreta Martinez, J.; Fuentes, P.; deMarti iOlius, A.; Garcia-Frias, J.; Rodríguez Fonollosa, J.; Crespo, P. M.
Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors Journal Article
In: Physical Review Research, vol. 5, iss. 3, 2023, ISBN: 2643-1564.
Abstract | Links | BibTeX | Tags: TECNUN
@article{nokey,
title = {Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors},
author = {Etxezarreta Martinez, J. and Fuentes, P. and deMarti iOlius, A. and Garcia-Frias, J. and Rodríguez Fonollosa, J. and Crespo, P.M.},
url = {https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.033055},
doi = {doi.org/10.1103/PhysRevResearch.5.033055},
isbn = {2643-1564},
year = {2023},
date = {2023-07-26},
journal = {Physical Review Research},
volume = {5},
issue = {3},
abstract = {Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (𝑇1) and dephasing times (𝑇2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of 𝑇1 and 𝑇2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.},
keywords = {TECNUN},
pubstate = {published},
tppubtype = {article}
}
Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (𝑇1) and dephasing times (𝑇2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of 𝑇1 and 𝑇2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.
