{"title":"Concatenate codes, save qubits","authors":"Satoshi Yoshida, Shiro Tamiya, Hayata Yamasaki","doi":"10.1038/s41534-025-01035-8","DOIUrl":"https://doi.org/10.1038/s41534-025-01035-8","url":null,"abstract":"<p>The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice other factors. Here, we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10<sup>−10</sup> and 10<sup>−24</sup> by more than 90% and 96%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.5% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"27 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144183756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luise Prielinger, Álvaro G. Iñesta, Gayane Vardoyan
{"title":"Surrogate-guided optimization in quantum networks","authors":"Luise Prielinger, Álvaro G. Iñesta, Gayane Vardoyan","doi":"10.1038/s41534-025-01048-3","DOIUrl":"https://doi.org/10.1038/s41534-025-01048-3","url":null,"abstract":"<p>When physical architectures become too complex for analytical study, numerical simulation proves essential to investigate quantum network behavior. Although highly informative, these simulations involve intricate numerical functions without known analytical forms, making traditional optimization techniques that assume continuity, differentiability, or convexity inapplicable. We introduce a more efficient computational framework that employs machine learning models as surrogates for the objective function. We demonstrate the effectiveness of our approach by applying it to three well-known optimization problems in quantum networking: allocating quantum memory across multiple nodes, tuning an experimental parameter in every physical link of a quantum entanglement switch, and finding effective protocol configurations in a large asymmetric quantum network. Our algorithm consistently outperforms Simulated Annealing and Bayesian optimization within the allotted time, improving results by up to 29% and 28%, respectively. Our framework will thus allow for more comprehensive quantum network studies, integrating surrogate-assisted optimization with existing quantum network simulators.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"8 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144188844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mafalda Ramôa, Panagiotis G. Anastasiou, Luis Paulo Santos, Nicholas J. Mayhall, Edwin Barnes, Sophia E. Economou
{"title":"Reducing the resources required by ADAPT-VQE using coupled exchange operators and improved subroutines","authors":"Mafalda Ramôa, Panagiotis G. Anastasiou, Luis Paulo Santos, Nicholas J. Mayhall, Edwin Barnes, Sophia E. Economou","doi":"10.1038/s41534-025-01039-4","DOIUrl":"https://doi.org/10.1038/s41534-025-01039-4","url":null,"abstract":"<p>Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the Noisy Intermediate-Scale Quantum era. Since the inception of the first such algorithm, the Adaptive Derivative-Assembled Problem-Tailored Variational Quantum Eigensolver (ADAPT-VQE), many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool—which we term Coupled Exchange Operator (CEO) pool—to assess the cost of running state-of-the-art ADAPT-VQE on hardware in terms of measurement counts and circuit depth. We show a dramatic reduction of these quantum computational resources compared to the early versions of the algorithm: CNOT count, CNOT depth and measurement costs are reduced by up to 88%, 96% and 99.6%, respectively, for molecules represented by 12 to 14 qubits (LiH, H<sub>6</sub> and BeH<sub>2</sub>). We also find that our state-of-the-art CEO-ADAPT-VQE outperforms the Unitary Coupled Cluster Singles and Doubles ansatz, the most widely used static VQE ansatz, in all relevant metrics, and offers a five order of magnitude decrease in measurement costs as compared to other static ansätze with competitive CNOT counts.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"3 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Control and readout of a 13-level trapped ion qudit","authors":"Pei Jiang Low, Brendan White, Crystal Senko","doi":"10.1038/s41534-025-01031-y","DOIUrl":"https://doi.org/10.1038/s41534-025-01031-y","url":null,"abstract":"<p>Scaling up the computational space of a quantum system is necessary to demonstrate quantum algorithmic advantage. Currently, including more information carriers is still a physical challenge in general. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with 13 computational states in our chosen information host, <sup>137</sup>Ba<sup>+</sup>. Utilizing the additional energy states found in <sup>137</sup>Ba<sup>+</sup> comes with non-trivial complexities which obscure the practical choices of energy states for qudit encoding. We report on tools we have developed for predicting energy states that are practical for qudit encoding, validated with good agreement with our experimental data. We also identify the major error sources for qudit control with <sup>137</sup>Ba<sup>+</sup> as avenues for improvement to achieve high fidelity operations.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"29 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144130268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Enrico Fontana, Manuel S. Rudolph, Ross Duncan, Ivan Rungger, Cristina Cîrstoiu
{"title":"Classical simulations of noisy variational quantum circuits","authors":"Enrico Fontana, Manuel S. Rudolph, Ross Duncan, Ivan Rungger, Cristina Cîrstoiu","doi":"10.1038/s41534-024-00955-1","DOIUrl":"https://doi.org/10.1038/s41534-024-00955-1","url":null,"abstract":"<p>Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, <span>lowesa</span> (low weight efficient simulation algorithm), for estimating expectation values of noisy parameterised quantum circuits with a fixed observable. It combines previous results on spectral analysis of parameterised circuits with Pauli back-propagation and recent ideas for simulations of noisy random circuits. We show, under some conditions on the circuits and mild assumptions on noise, that <span>lowesa</span> gives an efficient, polynomial algorithm in the number of qubits (and depth), with approximation error that vanishes exponentially in the physical error rate and a controllable cutoff parameter. This is valid for any expectation value that may be efficiently evaluated on a quantum computer. We discuss the practical limitations of the method for circuit classes with correlated parameters and its scaling with decreasing error rates.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"41 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiachen Chen, Yaozu Wu, Zhen Yang, Shibo Xu, Xuan Ye, Daili Li, Ke Wang, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Yu Gao, Ziqi Tan, Zhengyi Cui, Aosai Zhang, Ning Wang, Yiren Zou, Tingting Li, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Zixuan Song, Jinfeng Deng, Hang Dong, Pengfei Zhang, Wei Zhang, Hekang Li, Qiujiang Guo, Zhen Wang, Ying Li, Xiaoting Wang, Chao Song, H. Wang
{"title":"Quantum ensemble learning with a programmable superconducting processor","authors":"Jiachen Chen, Yaozu Wu, Zhen Yang, Shibo Xu, Xuan Ye, Daili Li, Ke Wang, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Yu Gao, Ziqi Tan, Zhengyi Cui, Aosai Zhang, Ning Wang, Yiren Zou, Tingting Li, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Zixuan Song, Jinfeng Deng, Hang Dong, Pengfei Zhang, Wei Zhang, Hekang Li, Qiujiang Guo, Zhen Wang, Ying Li, Xiaoting Wang, Chao Song, H. Wang","doi":"10.1038/s41534-025-01037-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01037-6","url":null,"abstract":"<p>Quantum machine learning is among the most exciting potential applications of quantum computing. However, the vulnerability of quantum information to environmental noises and the consequent high cost for realizing fault tolerance has impeded the quantum models from learning complex datasets. Here, we introduce AdaBoost.Q, a quantum adaptation of the classical adaptive boosting (AdaBoost) algorithm designed to enhance learning capabilities of quantum classifiers. Based on the probabilistic nature of quantum measurement, the algorithm improves the prediction accuracy by refining the attention mechanism during the adaptive training and combination of quantum classifiers. We experimentally demonstrate the versatility of our approach on a programmable superconducting processor, where we observe notable performance enhancements across various quantum machine learning models, including quantum neural networks and quantum convolutional neural networks. With AdaBoost.Q, we achieve an accuracy above 86% for a ten-class classification task over 10,000 test samples, and an accuracy of 100% for a quantum feature recognition task over 1564 test samples. Our results demonstrate a foundational tool for advancing quantum machine learning towards practical applications, which has broad applicability to both the current noisy and the future fault-tolerant quantum devices.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"55 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144104821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jamie Heredge, Niraj Kumar, Dylan Herman, Shouvanik Chakrabarti, Romina Yalovetzky, Shree Hari Sureshbabu, Changhao Li, Marco Pistoia
{"title":"Characterizing privacy in quantum machine learning","authors":"Jamie Heredge, Niraj Kumar, Dylan Herman, Shouvanik Chakrabarti, Romina Yalovetzky, Shree Hari Sureshbabu, Changhao Li, Marco Pistoia","doi":"10.1038/s41534-025-01022-z","DOIUrl":"https://doi.org/10.1038/s41534-025-01022-z","url":null,"abstract":"<p>Ensuring data privacy in machine learning models is critical, especially in distributed settings where model gradients are shared among multiple parties for collaborative learning. Motivated by the increasing success of recovering input data from the gradients of classical models, this study investigates the analogous challenge for variational quantum circuits (VQC) as quantum machine learning models. We highlight the crucial role of the dynamical Lie algebra (DLA) in determining privacy vulnerabilities. While the DLA has been linked to the trainability and simulatability of VQC models, we establish its connection to privacy for the first time. We show that properties conducive to VQC trainability, such as a polynomial-sized DLA, also facilitate extracting detailed snapshots of the input, posing a weak privacy breach. We further investigate conditions for a strong privacy breach, where original input data can be recovered from snapshots by classical or quantum-assisted methods. We establish properties of the encoding map, such as classical simulatability, overlap with DLA basis, and its Fourier frequency characteristics that enable such a privacy breach of VQC models. Our framework thus guides the design of quantum machine learning models, balancing trainability and robust privacy protection.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"15 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144097466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Meta-learning assisted robust control of universal quantum gates with uncertainties","authors":"Shihui Zhang, Zibo Miao, Yu Pan, Sibo Tao, Yu Chen","doi":"10.1038/s41534-025-01034-9","DOIUrl":"https://doi.org/10.1038/s41534-025-01034-9","url":null,"abstract":"<p>Achieving high-fidelity quantum gates is crucial for reliable quantum computing. However, decoherence and control pulse imperfections pose significant challenges in realizing the theoretical fidelity of quantum gates in practical systems. To address these challenges, we propose the meta-reinforcement learning quantum control algorithm (metaQctrl), which leverages a two-layer learning framework to enhance robustness and fidelity. The inner reinforcement learning network focuses on decision making for specific optimization problems, while the outer meta-learning network adapts to varying environments and provides feedback to the inner network. Our comparative analysis regarding the realization of universal quantum gates demonstrates that metaQctrl achieves higher fidelity with fewer control pulses than conventional methods in the presence of uncertainties. These results can contribute to the exploration of the quantum speed limit and facilitate the implementation of quantum circuits with system imperfections involved.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"234 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144097586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nicolas Gigena, Ekta Panwar, Giovanni Scala, Mateus Araújo, Máté Farkas, Anubhav Chaturvedi
{"title":"Self-testing tilted strategies for maximal loophole-free nonlocality","authors":"Nicolas Gigena, Ekta Panwar, Giovanni Scala, Mateus Araújo, Máté Farkas, Anubhav Chaturvedi","doi":"10.1038/s41534-025-01029-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01029-6","url":null,"abstract":"<p>The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For <i>any</i> Bell inequality and <i>any</i> specification of detection efficiencies, the optimal strategies are those that maximally violate a <i>tilted</i> version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the <i>doubly-tilted</i> versions of <i>Clauser-Horne-Shimony-Holt</i> inequality are <i>unique</i> up to local isometries. We utilize a Jordan’s lemma and Gröbner basis-based proof technique to analytically derive self-testing statements for the <i>entire</i> family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the <i>Navascués–Pironio–Acín</i> hierarchy to saturate the maximum quantum violation of these inequalities.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"135 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144097608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Machine learning message-passing for the scalable decoding of QLDPC codes","authors":"Arshpreet Singh Maan, Alexandru Paler","doi":"10.1038/s41534-025-01033-w","DOIUrl":"https://doi.org/10.1038/s41534-025-01033-w","url":null,"abstract":"<p>We present Astra, a novel and scalable decoder using graph neural networks. In general, Quantum Low Density Parity Check (QLDPC) decoding is based on Belief Propagation (BP, a variant of message-passing) and requires time intensive post-processing methods such as Ordered Statistics Decoding (OSD). Our decoder works on the Tanner graph, similarly to BP. Without using any post-processing, Astra achieves higher thresholds and better Logical Error Rates (LER) compared to BPOSD, both for surface codes trained up to distance 11 and Bivariate Bicycle (BB) codes trained up to distance 18. Moreover, we can successfully extrapolate the decoding functionality: we decode high distances (surface code up to distance 25 and BB code up to distance 34) by using decoders trained on lower distances. Extrapolated Astra achieves better LER than BPOSD for BB codes. Astra(+OSD) achieves orders of magnitude lower logical error rates for BB codes compared to BP(+OSD).</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"74 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144066906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}