Pub Date : 2026-01-09DOI: 10.1109/JSAIT.2026.3652821
{"title":"2025 Index Journal on Selected Areas in Information Theory","authors":"","doi":"10.1109/JSAIT.2026.3652821","DOIUrl":"https://doi.org/10.1109/JSAIT.2026.3652821","url":null,"abstract":"","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"470-478"},"PeriodicalIF":2.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11344831","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-03DOI: 10.1109/JSAIT.2025.3628112
Stephen Creagh;Valon Blakaj;Kangyu Zhao;Gabriele Gradoni
An approach to characterising operator spectra using a ray-dynamical phase space, originating from treatments of quantum mechanics, is adapted to calculate degrees of freedom and channel capacities of wireless communication between surfaces. The method is grounded on propagation of correlation functions and exploits the outputs of Eulerian ray-tracing algorithms. It presents results using a signal-to-noise ratio expressed as a function of phase space coordinates, resolving it in terms of direction as well as position. The ability of the phase-space representation to capture the spatial-angular dynamics of propagation makes the methodology suitable for advanced studies of electromagnetic signal and information theory. Examples are offered for flat as well as curved surfaces, communicating in free-space and in confined propagation environments.
{"title":"Electromagnetic Information Theory in Phase Space","authors":"Stephen Creagh;Valon Blakaj;Kangyu Zhao;Gabriele Gradoni","doi":"10.1109/JSAIT.2025.3628112","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3628112","url":null,"abstract":"An approach to characterising operator spectra using a ray-dynamical phase space, originating from treatments of quantum mechanics, is adapted to calculate degrees of freedom and channel capacities of wireless communication between surfaces. The method is grounded on propagation of correlation functions and exploits the outputs of Eulerian ray-tracing algorithms. It presents results using a signal-to-noise ratio expressed as a function of phase space coordinates, resolving it in terms of direction as well as position. The ability of the phase-space representation to capture the spatial-angular dynamics of propagation makes the methodology suitable for advanced studies of electromagnetic signal and information theory. Examples are offered for flat as well as curved surfaces, communicating in free-space and in confined propagation environments.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"446-457"},"PeriodicalIF":2.2,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-08DOI: 10.1109/JSAIT.2025.3619053
Krishna Gopal Benerjee;Adrish Banerjee
This paper presents constructions of DNA codes that satisfy biological and combinatorial constraints for DNA-based data storage systems. We introduce an algorithm that generates DNA blocks containing sequences that meet the required constraints for DNA codes. The constructed DNA sequences satisfy biological constraints: balanced GC-content, avoidance of secondary structures, and prevention of homopolymer runs. These sequences simultaneously satisfy combinatorial constraints that ensure differences among DNA sequences and their reverse and reverse-complement sequences. The DNA codes incorporate error correction through minimum Hamming distance requirements. We establish a bijective mapping between algebraic structures and DNA sequences, providing construction of DNA codes with specified characteristics. Using this framework, we construct DNA codes based on error-correcting codes, including Simplex and Reed-Muller codes. These constructions ensure DNA sequences avoid secondary structures and homopolymer runs exceeding length three, which cause errors in DNA storage systems. Concatenated sequences maintain these properties. The codes achieve non-vanishing code rates and minimum Hamming distances for large sequence lengths, demonstrating viability for DNA-based data storage systems.
{"title":"On Algebraic Designing of DNA Codes With Biological and Combinatorial Constraints","authors":"Krishna Gopal Benerjee;Adrish Banerjee","doi":"10.1109/JSAIT.2025.3619053","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3619053","url":null,"abstract":"This paper presents constructions of DNA codes that satisfy biological and combinatorial constraints for DNA-based data storage systems. We introduce an algorithm that generates DNA blocks containing sequences that meet the required constraints for DNA codes. The constructed DNA sequences satisfy biological constraints: balanced GC-content, avoidance of secondary structures, and prevention of homopolymer runs. These sequences simultaneously satisfy combinatorial constraints that ensure differences among DNA sequences and their reverse and reverse-complement sequences. The DNA codes incorporate error correction through minimum Hamming distance requirements. We establish a bijective mapping between algebraic structures and DNA sequences, providing construction of DNA codes with specified characteristics. Using this framework, we construct DNA codes based on error-correcting codes, including Simplex and Reed-Muller codes. These constructions ensure DNA sequences avoid secondary structures and homopolymer runs exceeding length three, which cause errors in DNA storage systems. Concatenated sequences maintain these properties. The codes achieve non-vanishing code rates and minimum Hamming distances for large sequence lengths, demonstrating viability for DNA-based data storage systems.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"432-445"},"PeriodicalIF":2.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145405299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-06DOI: 10.1109/JSAIT.2025.3616940
Jin Sima;Chao Pan;S. Kasra Tabatabaei;Alvaro G. Hernandez;Charles M. Schroeder;Olgica Milenkovic
DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards system, which introduces nicks (cuts) in the DNA backbone, encodes only one bit per nicking site, limiting density. We propose DNA Tails, a storage paradigm that encodes nonbinary symbols at nicking sites by growing enzymatically synthesized single-stranded DNA of varied lengths. The average tail lengths encode multiple information bits and are controlled via a staggered nicking-tail extension process. We demonstrate the feasibility of this encoding approach experimentally and identify common sources of errors, such as calibration errors and stumped tail growth errors. To mitigate calibration errors, we use rank modulation proposed for flash memory. To correct stumped tail growth errors, we introduce a new family of rank modulation codes that can correct “stuck-at” errors. Our analytical results include constructions for order-optimal-redundancy permutation codes and accompanying encoding and decoding algorithms.
{"title":"DNA Tails for Molecular Flash Memory","authors":"Jin Sima;Chao Pan;S. Kasra Tabatabaei;Alvaro G. Hernandez;Charles M. Schroeder;Olgica Milenkovic","doi":"10.1109/JSAIT.2025.3616940","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3616940","url":null,"abstract":"DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards system, which introduces nicks (cuts) in the DNA backbone, encodes only one bit per nicking site, limiting density. We propose DNA Tails, a storage paradigm that encodes nonbinary symbols at nicking sites by growing enzymatically synthesized single-stranded DNA of varied lengths. The average tail lengths encode multiple information bits and are controlled via a staggered nicking-tail extension process. We demonstrate the feasibility of this encoding approach experimentally and identify common sources of errors, such as calibration errors and stumped tail growth errors. To mitigate calibration errors, we use rank modulation proposed for flash memory. To correct stumped tail growth errors, we introduce a new family of rank modulation codes that can correct “stuck-at” errors. Our analytical results include constructions for order-optimal-redundancy permutation codes and accompanying encoding and decoding algorithms.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"458-469"},"PeriodicalIF":2.2,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-03DOI: 10.1109/JSAIT.2025.3617251
Zitan Chen
The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all possible lengths of the string. In this work, we present binary codes of length $n$ in which every codeword can be efficiently reconstructed from its erroneous prefix-suffix compositions with at most $t$ composition errors. All our constructions have decoding complexity polynomial in $n$ and the best of our constructions has constant rate and can correct $t=Theta (n)$ errors. As a comparison, no prior constructions can afford to efficiently correct $t=Theta (n)$ arbitrary composition errors. Additionally, we propose a method of encoding $h$ arbitrary strings of the same length so that they can be reconstructed from the multiset union of their error-free prefix-suffix compositions, at the expense of $h$ -fold coding overhead. In contrast, existing methods can only recover $h$ distinct strings, albeit with code rate asymptotically equal to $1/h$ . Building on the top of the proposed method, we also present a coding scheme that enables efficient recovery of $h$ strings from their erroneous prefix-suffix compositions with $t=Theta (n)$ errors.
{"title":"Coding Methods for String Reconstruction From Erroneous Prefix-Suffix Compositions","authors":"Zitan Chen","doi":"10.1109/JSAIT.2025.3617251","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3617251","url":null,"abstract":"The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all possible lengths of the string. In this work, we present binary codes of length <inline-formula> <tex-math>$n$ </tex-math></inline-formula> in which every codeword can be efficiently reconstructed from its erroneous prefix-suffix compositions with at most <inline-formula> <tex-math>$t$ </tex-math></inline-formula> composition errors. All our constructions have decoding complexity polynomial in <inline-formula> <tex-math>$n$ </tex-math></inline-formula> and the best of our constructions has constant rate and can correct <inline-formula> <tex-math>$t=Theta (n)$ </tex-math></inline-formula> errors. As a comparison, no prior constructions can afford to efficiently correct <inline-formula> <tex-math>$t=Theta (n)$ </tex-math></inline-formula> arbitrary composition errors. Additionally, we propose a method of encoding <inline-formula> <tex-math>$h$ </tex-math></inline-formula> arbitrary strings of the same length so that they can be reconstructed from the multiset union of their error-free prefix-suffix compositions, at the expense of <inline-formula> <tex-math>$h$ </tex-math></inline-formula>-fold coding overhead. In contrast, existing methods can only recover <inline-formula> <tex-math>$h$ </tex-math></inline-formula> distinct strings, albeit with code rate asymptotically equal to <inline-formula> <tex-math>$1/h$ </tex-math></inline-formula>. Building on the top of the proposed method, we also present a coding scheme that enables efficient recovery of <inline-formula> <tex-math>$h$ </tex-math></inline-formula> strings from their erroneous prefix-suffix compositions with <inline-formula> <tex-math>$t=Theta (n)$ </tex-math></inline-formula> errors.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"394-402"},"PeriodicalIF":2.2,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-29DOI: 10.1109/JSAIT.2025.3613272
Tomer Cohen;Eitan Yaakobi
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. The first problem studies the expected number of strand reads in order to decode a composite strand or a group of composite strands. In the second problem, our goal is study how to carefully choose a fixed number of mixtures of the DNA nucleotides such that the decoding probability by the maximum likelihood decoder is maximized.
{"title":"Optimizing the Decoding Probability and Coverage Ratio of Composite DNA","authors":"Tomer Cohen;Eitan Yaakobi","doi":"10.1109/JSAIT.2025.3613272","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3613272","url":null,"abstract":"This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. The first problem studies the expected number of strand reads in order to decode a composite strand or a group of composite strands. In the second problem, our goal is study how to carefully choose a fixed number of mixtures of the DNA nucleotides such that the decoding probability by the maximum likelihood decoder is maximized.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"417-431"},"PeriodicalIF":2.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145405334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-16DOI: 10.1109/JSAIT.2025.3610751
Ziv Aharoni;Henry D. Pfister
Synchronization errors, arising from both synthesis and sequencing noise, present a fundamental challenge in DNA-based data storage systems. These errors are often modeled as insertion-deletion-substitution (IDS) channels, for which maximum-likelihood decoding is quite computationally expensive. In this work, we propose a data-driven approach based on neural polar decoders (NPDs) to design decoders with reduced complexity for channels with synchronization errors. The proposed architecture enables decoding over IDS channels with reduced complexity $O(A N log N)$ , where $A$ is a tunable parameter independent of the channel. NPDs require only sample access to the channel and can be trained without an explicit channel model. Additionally, NPDs provide mutual information (MI) estimates that can be used to optimize input distributions and code design. We demonstrate the effectiveness of NPDs on both synthetic deletion and IDS channels. For deletion channels, we show that NPDs achieve near-optimal decoding performance and accurate MI estimation, with significantly lower complexity than trellis-based decoders. We also provide numerical estimates of the channel capacity for the deletion channel. We extend our evaluation to realistic DNA storage settings, including channels with multiple noisy reads and real-world Nanopore sequencing data. Our results show that NPDs match or surpass the performance of existing methods while using significantly fewer parameters than the state-of-the-art. These findings highlight the promise of NPDs for robust and efficient decoding in DNA data storage systems.
由合成噪声和测序噪声引起的同步误差是基于dna的数据存储系统面临的一个基本挑战。这些错误通常被建模为插入-删除-替换（IDS）通道，对于这些通道，最大似然解码在计算上非常昂贵。在这项工作中，我们提出了一种基于神经极性解码器（npd）的数据驱动方法，用于设计具有同步错误的信道的解码器，降低了解码器的复杂性。所提出的体系结构使IDS信道上的解码具有较低的复杂度$O(A N log N)$，其中$A$是一个独立于信道的可调参数。npd只需要访问通道的样本，并且可以在没有显式通道模型的情况下进行训练。此外，npd提供可用于优化输入分布和代码设计的互信息（MI）估计。我们证明了npd在合成缺失和IDS通道上的有效性。对于删除信道，我们表明npd实现了近乎最佳的解码性能和准确的MI估计，其复杂性明显低于基于网格的解码器。我们还提供了删除信道的信道容量的数值估计。我们将我们的评估扩展到现实的DNA存储设置，包括具有多个噪声读取的通道和真实的纳米孔测序数据。我们的研究结果表明，npd在使用比最先进的参数少得多的情况下，达到或超过了现有方法的性能。这些发现突出了npd在DNA数据存储系统中稳健和高效解码的前景。
{"title":"Neural Polar Decoders for DNA Data Storage","authors":"Ziv Aharoni;Henry D. Pfister","doi":"10.1109/JSAIT.2025.3610751","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3610751","url":null,"abstract":"Synchronization errors, arising from both synthesis and sequencing noise, present a fundamental challenge in DNA-based data storage systems. These errors are often modeled as insertion-deletion-substitution (IDS) channels, for which maximum-likelihood decoding is quite computationally expensive. In this work, we propose a data-driven approach based on neural polar decoders (NPDs) to design decoders with reduced complexity for channels with synchronization errors. The proposed architecture enables decoding over IDS channels with reduced complexity <inline-formula> <tex-math>$O(A N log N)$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$A$ </tex-math></inline-formula> is a tunable parameter independent of the channel. NPDs require only sample access to the channel and can be trained without an explicit channel model. Additionally, NPDs provide mutual information (MI) estimates that can be used to optimize input distributions and code design. We demonstrate the effectiveness of NPDs on both synthetic deletion and IDS channels. For deletion channels, we show that NPDs achieve near-optimal decoding performance and accurate MI estimation, with significantly lower complexity than trellis-based decoders. We also provide numerical estimates of the channel capacity for the deletion channel. We extend our evaluation to realistic DNA storage settings, including channels with multiple noisy reads and real-world Nanopore sequencing data. Our results show that NPDs match or surpass the performance of existing methods while using significantly fewer parameters than the state-of-the-art. These findings highlight the promise of NPDs for robust and efficient decoding in DNA data storage systems.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"403-416"},"PeriodicalIF":2.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145405347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-16DOI: 10.1109/JSAIT.2025.3610643
Hsin-Po Wang;Venkatesan Guruswami
As a potential implementation of data storage using DNA molecules, multiple strands of DNA are stored unordered in a liquid container. When the data are needed, an array of DNA readers will sample the strands with replacement, producing a Poisson-distributed number of noisy reads for each strand. The primary challenge here is to design an algorithm that reconstructs data from these unsorted, repetitive, and noisy reads. In this paper, we lay down a capacity-achieving rateless code along each strand to encode its index; we then lay down a capacity-achieving block code at the same position across all strands to protect the data. These codes weave a low-complexity storage scheme that saturates the fundamental upper limit of DNA. This improves upon the previous work of Weinberger and Merhav, which proves said bound and uses high-complexity random codes to saturate the limit. Our scheme also differs from other concatenation-based implementations of DNA data storage in the sense that, instead of decoding the inner codes first and passing the results to the outer code, our decoder alternates between the rateless codes and the block codes.
{"title":"Geno-Weaving: A Framework for Low-Complexity Capacity-Achieving DNA Data Storage","authors":"Hsin-Po Wang;Venkatesan Guruswami","doi":"10.1109/JSAIT.2025.3610643","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3610643","url":null,"abstract":"As a potential implementation of data storage using DNA molecules, multiple strands of DNA are stored unordered in a liquid container. When the data are needed, an array of DNA readers will sample the strands with replacement, producing a Poisson-distributed number of noisy reads for each strand. The primary challenge here is to design an algorithm that reconstructs data from these unsorted, repetitive, and noisy reads. In this paper, we lay down a capacity-achieving rateless code along each strand to encode its index; we then lay down a capacity-achieving block code at the same position across all strands to protect the data. These codes weave a low-complexity storage scheme that saturates the fundamental upper limit of DNA. This improves upon the previous work of Weinberger and Merhav, which proves said bound and uses high-complexity random codes to saturate the limit. Our scheme also differs from other concatenation-based implementations of DNA data storage in the sense that, instead of decoding the inner codes first and passing the results to the outer code, our decoder alternates between the rateless codes and the block codes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"383-393"},"PeriodicalIF":2.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-25DOI: 10.1109/JSAIT.2025.3602446
Zhuangzhuang Chen;Narayanan Rengaswamy
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known $[![n,n-2,2]!]$ error-detecting code family. Our analysis shows that this family implements Trotter circuits with essentially optimal depth under reasonable assumptions, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. Importantly, the solve-and-stitch algorithm has the potential to scale beyond this specific example, as illustrated by a generalization to the four-qubit logical Clifford Trotter circuit on the $[![{ 20,4,2 }]!] $ hypergraph product code, thereby providing a principled approach to tailored fault-tolerance in quantum computing.
{"title":"Tailoring Fault-Tolerance to Quantum Algorithms","authors":"Zhuangzhuang Chen;Narayanan Rengaswamy","doi":"10.1109/JSAIT.2025.3602446","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3602446","url":null,"abstract":"The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known <inline-formula> <tex-math>$[![n,n-2,2]!]$ </tex-math></inline-formula> error-detecting code family. Our analysis shows that this family implements Trotter circuits with essentially optimal depth under reasonable assumptions, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. Importantly, the solve-and-stitch algorithm has the potential to scale beyond this specific example, as illustrated by a generalization to the four-qubit logical Clifford Trotter circuit on the <inline-formula> <tex-math>$[![{ 20,4,2 }]!] $ </tex-math></inline-formula> hypergraph product code, thereby providing a principled approach to tailored fault-tolerance in quantum computing.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"311-324"},"PeriodicalIF":2.2,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144998382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical $[n,k,d ge m+1]$ binary linear code with certain additional properties, we show that pure $[[n,k,m+1]]_{2}$ quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure $[[{2^{2r}-1,2^{2r}-2r-3,3}]]_{2}$ and $[[(2^{4r}-1)^{2}, (2^{4r}-1)^{2} - 32r-7, 5]]_{2}$ QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.
{"title":"Codeword Stabilized Codes From m-Uniform Graph States","authors":"Sowrabh Sudevan;Sourin Das;Thamadathil Aswanth;Nupur Patanker;Navin Kashyap","doi":"10.1109/JSAIT.2025.3602744","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3602744","url":null,"abstract":"An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical <inline-formula> <tex-math>$[n,k,d ge m+1]$ </tex-math></inline-formula> binary linear code with certain additional properties, we show that pure <inline-formula> <tex-math>$[[n,k,m+1]]_{2}$ </tex-math></inline-formula> quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure <inline-formula> <tex-math>$[[{2^{2r}-1,2^{2r}-2r-3,3}]]_{2}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$[[(2^{4r}-1)^{2}, (2^{4r}-1)^{2} - 32r-7, 5]]_{2}$ </tex-math></inline-formula> QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"296-310"},"PeriodicalIF":2.2,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144998383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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