Ridho Nur Rohman Wijaya;Budi Setiyono;Dwi Ratna Sulistyaningrum
{"title":"Hybrid Quantum Capsule Network: Quantum Transformation Circuit as Vote Transformation in Image Classification","authors":"Ridho Nur Rohman Wijaya;Budi Setiyono;Dwi Ratna Sulistyaningrum","doi":"10.1109/TQE.2026.3709247","DOIUrl":"https://doi.org/10.1109/TQE.2026.3709247","url":null,"abstract":"A capsule network (CapsNet) provides a richer hierarchical representation than conventional neural networks through vector-shaped capsules and intercapsule routing. However, most CapsNet designs still rely on classic matrix-multiplication-based vote transformations, which limit the formation of the prediction vector to linear mappings in Euclidean space. In this article, we propose the hybrid quantum capsule network (HQCapsNet), an architecture that replaces classical vote transformations with a quantum transformation circuit (QTC) based on a parameterized quantum circuit (PQC). We introduce a QTC in two schemes: classwise QTC and fully connected QTC. Furthermore, the routing agreement mechanism is extended via hybrid quantum routing, leveraging various quantum similarity metrics. The evaluation was conducted on several binary image classification datasets, with MNIST, TMNIST, and MNIST-M used as the primary datasets. The experimental analysis included benchmarking of quantum embedding variations, the PQC ansatz, qubit-count analysis, circuit depth, and routing iterations. The experimental results show that the fully connected QTC is the best configuration, achieving consistent accuracy improvements over the classwise QTC, with the most significant improvement from 92.86% to 97.62% on the MNIST-M dataset. Compared to the classical CapsNet, the HQCapsNet also achieves higher performance across all primary datasets, achieving 99.95% accuracy on MNIST and competing with quantum–classical models on comparable split data. These results indicate that integrating quantum computing at the voting transformation step is a promising approach to improving CapsNet’s representation and generalization capabilities.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"3104025-3104025"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11593449","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148626129","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}
Thomas Scarinzi;Davide Orsucci;Marco Ferrari;Luca Barletta
{"title":"Boosting Information Reconciliation for Decoy-State Quantum Key Distribution Over a Satellite Downlink Channel","authors":"Thomas Scarinzi;Davide Orsucci;Marco Ferrari;Luca Barletta","doi":"10.1109/TQE.2026.3715957","DOIUrl":"https://doi.org/10.1109/TQE.2026.3715957","url":null,"abstract":"Quantum Key Distribution (QKD) is a cryptographic solution that leverages the properties of quantum mechanics to be resistant and secure even against an attacker with unlimited computational power. Satellite-based links are important in QKD because they can reach distances that the best fiber systems cannot. However, links between satellites in low Earth orbit and ground stations have a duration of only a few minutes, resulting in the generation of a small amount of secure keys. In this context, we investigate the optimization of the information reconciliation step of the QKD postprocessing in order to generate as much secure key as possible. As a first step, we build an accurate model of the downlink signal and Quantum Bit Error Rate (QBER) during a complete satellite pass, which are time-varying due to three effects: 1 the varying link geometry over time; 2) the scintillation effect; and 3) the different signal intensities adopted in the Decoy-State protocol. Leveraging the a priori information on the instantaneous QBER, we improve the efficiency of information reconciliation (i.e., the error correction phase) in the Decoy-State BB84 protocol, resulting in a secure key that is almost 3% longer for realistic scenarios, with no computational or hardware complexity overhead.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"4101812-4101812"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11617353","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148836543","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}
Andreea-Iulia Lefterovici;Michael Perk;Debora Ramacciotti;Antonio F. Rotundo;Shawn E. Skelton;Martin Steinbach
{"title":"Beyond Asymptotic Scaling: Comparing Functional Quantum Linear Solvers","authors":"Andreea-Iulia Lefterovici;Michael Perk;Debora Ramacciotti;Antonio F. Rotundo;Shawn E. Skelton;Martin Steinbach","doi":"10.1109/TQE.2026.3674210","DOIUrl":"https://doi.org/10.1109/TQE.2026.3674210","url":null,"abstract":"Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume fault-tolerant quantum computers, so they cannot yet be benchmarked on real hardware. Because an algorithm with better asymptotic scaling can underperform on instances of practical interest, the question of which of these algorithms is the most promising remains open. In this work, we implement a method to partially address this question. We consider four well-known QLS algorithms which directly implement an approximate matrix inversion function: the Harrow–Hassidim–Lloyd (HHL) algorithm, two algorithms utilizing a linear combination of unitaries, and one utilizing the quantum singular value transformation. These methods, known as functional QLS, share nearly identical assumptions about the problem setup and oracle access. Their computational cost is dominated by query calls to a matrix oracle encoding the problem one wants to solve. We provide formulas to count the number of queries needed to solve specific problem instances; these can be used to benchmark the algorithms on real-life instances, under benevolent, idealized assumptions, without requiring access to quantum hardware to implement the procedure. We select three data sets: random generated instances that obey the assumptions of functional QLS, linear systems from simplex iterations on the Mixed Integer Programming Library, and Poisson equations. Our methods can be easily extended to other data sets and provide a high-level guide to evaluate the performance of a QLS algorithm. In particular, our work shows that HHL underperforms in comparison to the other methods across all datasets, often by orders of magnitude, while the Chebyshev-approximation-based methods typically have the best performance.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"1-26"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11434996","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148480131","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}
{"title":"Quantum Communication Complexity of Regularized Linear Regression Protocols","authors":"Sayaki Matsushita","doi":"10.1109/TQE.2026.3687237","DOIUrl":"https://doi.org/10.1109/TQE.2026.3687237","url":null,"abstract":"Linear regression is fundamental to statistical analysis and machine learning, but its application to large-scale datasets necessitates distributed computing. The problem also arises in quantum computing, where handling extensive data requires distributed approaches. This article investigates distributed linear regression in the quantum coordinator model. Building upon the distributed quantum least-squares protocol developed by Montanaro and Shao (2024), this article proposes improved and extended quantum protocols for solving both ordinary (unregularized) and L2-regularized (Tikhonov) least-squares problems. For ordinary least-squares methods, the proposed protocol reduces the quantum communication complexity compared to the previous protocol. In particular, this yields a quadratic improvement in the number of digits of precision required for the generated quantum states. This improvement is achieved by incorporating advanced techniques such as branch marking and branch-marked gapped phase estimation developed by Low and Su (2026). Furthermore, this article establishes a setting for the L2-regularized least-squares problem specifically in the quantum coordinator model and derives its quantum communication complexity. The effect of regularization parameters on the quantum communication complexity is analyzed.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"3103012-3103012"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11494295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148480380","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}
Neel Malvania;Garry Jacyna;Bonnie L. Schmittberger Marlow;Zachary N. Hardesty-Shaw;Kathryn L. Nicolich;Kelly M. Backes;Jamie L. MacLennan;Charlie T. Fancher
{"title":"Rydberg Atom Electric Field Sensors as Linear Time-Invariant Systems","authors":"Neel Malvania;Garry Jacyna;Bonnie L. Schmittberger Marlow;Zachary N. Hardesty-Shaw;Kathryn L. Nicolich;Kelly M. Backes;Jamie L. MacLennan;Charlie T. Fancher","doi":"10.1109/TQE.2026.3721420","DOIUrl":"https://doi.org/10.1109/TQE.2026.3721420","url":null,"abstract":"Over the past decade, Rydberg atom electric field sensors have been under investigation as potential alternatives or complements to conventional antenna-based receivers for selected applications in RF communications, remote sensing, and precision metrology. To understand the potential utility of these devices for various use cases, it is crucial to develop models that accurately predict key performance metrics, such as instantaneous bandwidth and dynamic range. However, existing numerical models require solving a large set of coupled differential equations that is computationally intensive and lengthy to solve. We present an analytic approach that can be used to derive an impulse response function that allows up to two orders-of-magnitude reduction in computation time compared to the full time-dependent integration of the equations of motion. This approach can be used to enable rapid assessments of the Rydberg sensor’s response to various waveforms.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"1-11"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11643613","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148925256","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}
{"title":"Network-Based Quantum Computing: An Efficient Design Framework for Many-Small-Node Distributed Fault-Tolerant Quantum Computing","authors":"Soshun Naito;Yasunari Suzuki;Yuuki Tokunaga","doi":"10.1109/TQE.2026.3722428","DOIUrl":"https://doi.org/10.1109/TQE.2026.3722428","url":null,"abstract":"In fault-tolerant quantum computing, a large number of physical qubits are required to construct a single logical qubit, and a single quantum node may be able to hold only a small number of logical qubits. In such a case, the idea of distributed fault-tolerant quantum computing (DFTQC) is important to demonstrate large-scale quantum computing using small-scale nodes. However, the design of distributed systems on small-scale nodes, where each node can store only one or a few logical qubits for computation, has not been explored well yet. In this article, we propose network-based quantum computing (NBQC) to efficiently realize distributed fault-tolerant quantum computing using many small-scale nodes. A key idea of NBQC is to let computational data continuously move throughout the network while maintaining the connectivity to other nodes. We numerically show that for practical benchmark tasks, our method achieves shorter execution times than circuit-based strategies and more node-efficient constructions than measurement-based quantum computing. Also, if we are allowed to specialize the network to the structure of quantum programs, such as peak access frequencies, the number of nodes can be significantly reduced. Thus, our methods provide a foundation in designing DFTQC architecture exploiting the redundancy of many small fault-tolerant nodes.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"3104632-3104632"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11646996","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148925347","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}
Pavel Rytíř;Phillip C. Burke;Christos Aravanis;Jiří Vala;Jakub Mareček
{"title":"Topological Quantum Compilation Using Mixed-Integer Programming","authors":"Pavel Rytíř;Phillip C. Burke;Christos Aravanis;Jiří Vala;Jakub Mareček","doi":"10.1109/TQE.2026.3710775","DOIUrl":"https://doi.org/10.1109/TQE.2026.3710775","url":null,"abstract":"Quantum computation offers the potential to solve certain problems faster than classical computing, but its practical realization is hindered by significant challenges associated with error propagation and decoherence. Topological quantum computing addresses these issues by encoding qubits in particular 2-D topological condensed matter systems, effectively described by topological quantum field theories, where quantum gates are implemented through sequences of braids of quasi-particles with exotic fractional statistics. The explicit construction of these sequences is a nontrivial task. In this work, we introduce a general optimization framework for a broad class of quantum compilation problems, including the compilation of quantum gates in topological quantum computing. The framework is based on Mixed-Integer QuadraticallyConstrained Quadratic Programming, which employs convex relaxations to tackle the underlying nonconvex optimization problem. We demonstrate the effectiveness of this framework by compiling a quantum gate from the local equivalence class of the controlled-<sc>not</small> operation for a nonsemisimple topological field theory for the first time. Our results provide a constructive pathway from abstract universality proofs to explicit gate implementations, as a practical tool in topological quantum compilation.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"3104212-3104212"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11596585","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148747165","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}
Jordi Pérez-Guijarro;Alba Pagès-Zamora;Javier R. Fonollosa
{"title":"Extension of Clifford Data Regression Methods for Quantum Error Mitigation","authors":"Jordi Pérez-Guijarro;Alba Pagès-Zamora;Javier R. Fonollosa","doi":"10.1109/TQE.2026.3677541","DOIUrl":"https://doi.org/10.1109/TQE.2026.3677541","url":null,"abstract":"To address the challenge posed by noise in real quantum devices, quantum error mitigation techniques play a crucial role. These techniques are resource-efficient, making them suitable for implementation in noisy intermediate-scale quantum devices, unlike the more resource-intensive quantum error correction codes. A notable example of such a technique is Clifford Data Regression, which employs a supervised learning approach. This work investigates two variants of this technique, both of which introduce a nontrivial set of gates into the original circuit. The first variant uses multiple copies of the original circuit, while the second adds a layer of single-qubit rotations. Different characteristics of these methods are analyzed theoretically, such as their complexity or the scaling of the error with various parameters. In addition, the performance of these methods is evaluated through numerical experiments, demonstrating a reduction in root mean square error.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"1-22"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11456224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148482043","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}
{"title":"Mitigating Precision Errors in Quantum Annealing via Coefficient Reduction of Embedded Hamiltonians","authors":"Kentaro Ohno;Nozomu Togawa","doi":"10.1109/TQE.2026.3678999","DOIUrl":"https://doi.org/10.1109/TQE.2026.3678999","url":null,"abstract":"Quantum annealing is a quantum algorithm to solve combinatorial optimization problems. In the current quantum annealing devices, the dynamic range of the input Ising Hamiltonian, defined as the ratio of the largest to the smallest coefficient, significantly affects the quality of the output solution due to limited hardware precision. Several methods have been proposed to reduce the dynamic range by reducing large coefficients in the Ising Hamiltonian. However, existing studies do not take into account minor embedding, which is an essential process in current quantum annealers. In this study, we revisit three existing coefficient-reduction methods under the constraints of minor embedding. We evaluate to what extent these methods reduce the dynamic range of the minor-embedded Hamiltonian and improve the sample quality obtained from the D-Wave Advantage quantum annealer. The results show that, on the set of problems tested in this study, the interaction-extension method effectively improves the sample quality by reducing the dynamic range, while the bounded-coefficient integer encoding and the augmented Lagrangian method have only limited effects. Furthermore, we empirically show that reducing external field coefficients at the logical Hamiltonian level is not required in practice, since minor embedding automatically has the role of reducing them. These findings suggest future directions for enhancing the sample quality of quantum annealers by suppressing hardware errors through preprocessing of the input problem.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"1-22"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11458840","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148479749","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}
{"title":"Perfect Quantum Teleportation in Memory Amplitude-Damping Channels Based on Preflipping and Environment-Assisted Measurement","authors":"Shiye Zhang;Sajede Harraz;Sen Kuang;Shuang Cong","doi":"10.1109/TQE.2026.3694290","DOIUrl":"https://doi.org/10.1109/TQE.2026.3694290","url":null,"abstract":"Most of the existing quantum teleportation schemes do not consider the memory effect of noise, which is becoming increasingly serious in practical quantum communication. In this article, we propose two quantum teleportation protocols for noisy memory channels: one based on preflipping (PF) and another incorporating preflipping with environment-assisted measurement (PF-EAM). In the PF protocol, a PF operation is applied to the entangled qubits before entanglement distribution to enhance robustness against noise. A recovery operator is then used to reverse the PF operation. In the PF-EAM protocol, environment-assisted measurement (EAM) is added to the entanglement distribution process, further improving teleportation fidelity. Since the PF operator in the two protocols is a fixed unitary operator, our protocols exclude additional parameters, which is unlike weak measurement (WM) schemes that rely on adjustable measurement strength. We derive analytical expressions for the average fidelity and the success probability of our teleportation protocols. The results show that the PF operator in the PF protocol effectively enhances the average fidelity of quantum teleportation in a deterministic manner, while the fidelity of PF-EAM remains at constant 1, unaffected by the noise intensity in the channel. In addition, our PF-EAM achieves a higher success probability while maintaining the fidelity of 1 with respect to the existing unprotected teleportation protocol, the protocol based on WM and measurement reversal (WM-MR), and the protocol based on the quantum feedforward control and EAM (QFFC-EAM) framework.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"7 ","pages":"4101216-4101216"},"PeriodicalIF":4.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11523148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148480473","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}