Pub Date : 2026-02-24DOI: 10.1038/s41534-026-01194-2
Mengzhen Ren, Yu-Cheng Chen, Ching-Jui Lai, Min-Hsiu Hsieh, Alice Hu
{"title":"Hybrid quantum-classical clustering for preparing a prior distribution of eigenspectrum","authors":"Mengzhen Ren, Yu-Cheng Chen, Ching-Jui Lai, Min-Hsiu Hsieh, Alice Hu","doi":"10.1038/s41534-026-01194-2","DOIUrl":"https://doi.org/10.1038/s41534-026-01194-2","url":null,"abstract":"","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"16 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147278936","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}
Pub Date : 2026-02-23DOI: 10.1038/s41534-026-01206-1
Etienne Granet, Yuta Kikuchi, Henrik Dreyer, Enrico Rinaldi
The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated quantum system that shows a strong signature of quantum chaos. Due to its chaotic nature, the simulation of real-time dynamics becomes quickly intractable by means of classical numerics, and thus, quantum simulation is deemed to be an attractive alternative. Nevertheless, quantum simulations of the SYK model on noisy quantum processors are severely limited by the complexity of its Hamiltonian. In this work, we simulate the real-time dynamics of a sparsified version of the SYK model with 24 Majorana fermions on a trapped-ion quantum processor. We adopt a randomized quantum algorithm, TETRIS, and develop an error mitigation technique tailored to the algorithm. Leveraging the hardware’s high-fidelity quantum operations and all-to-all connectivity of the qubits, we successfully calculate the Loschmidt amplitude for sufficiently long times so that its decay is observed. Based on the experimental and further numerical results, we assess the future possibility of larger-scale simulations of the SYK model by estimating the required quantum resources. Moreover, we present a scalable mirror-circuit benchmark based on the randomized SYK Hamiltonian and the TETRIS algorithm, which we argue provides a better estimate of the decay of fidelity for local observables than standard mirror-circuits.
{"title":"Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer","authors":"Etienne Granet, Yuta Kikuchi, Henrik Dreyer, Enrico Rinaldi","doi":"10.1038/s41534-026-01206-1","DOIUrl":"https://doi.org/10.1038/s41534-026-01206-1","url":null,"abstract":"The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated quantum system that shows a strong signature of quantum chaos. Due to its chaotic nature, the simulation of real-time dynamics becomes quickly intractable by means of classical numerics, and thus, quantum simulation is deemed to be an attractive alternative. Nevertheless, quantum simulations of the SYK model on noisy quantum processors are severely limited by the complexity of its Hamiltonian. In this work, we simulate the real-time dynamics of a sparsified version of the SYK model with 24 Majorana fermions on a trapped-ion quantum processor. We adopt a randomized quantum algorithm, TETRIS, and develop an error mitigation technique tailored to the algorithm. Leveraging the hardware’s high-fidelity quantum operations and all-to-all connectivity of the qubits, we successfully calculate the Loschmidt amplitude for sufficiently long times so that its decay is observed. Based on the experimental and further numerical results, we assess the future possibility of larger-scale simulations of the SYK model by estimating the required quantum resources. Moreover, we present a scalable mirror-circuit benchmark based on the randomized SYK Hamiltonian and the TETRIS algorithm, which we argue provides a better estimate of the decay of fidelity for local observables than standard mirror-circuits.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"104 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147278939","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}
Pub Date : 2026-02-21DOI: 10.1038/s41534-025-01157-z
Jun Qi, Chao-Han Huck Yang, Pin-Yu Chen, Min-Hsiu Hsieh
Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to the presence of barren plateaus and its sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Grounded in Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.
{"title":"TensorHyper-VQC: a tensor-train-guided hypernetwork for robust and scalable variational quantum computing","authors":"Jun Qi, Chao-Han Huck Yang, Pin-Yu Chen, Min-Hsiu Hsieh","doi":"10.1038/s41534-025-01157-z","DOIUrl":"https://doi.org/10.1038/s41534-025-01157-z","url":null,"abstract":"Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to the presence of barren plateaus and its sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Grounded in Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"103 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146260722","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}
Pub Date : 2026-02-19DOI: 10.1038/s41534-025-01168-w
Joseph Peetz, Scott E. Smart, Prineha Narang
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit dilations. This naturally enables simulations of open systems, which we demonstrate by preparing damped many-qubit GHZ states on ibm_hanoi. The technique further inspires two Hamiltonian simulation algorithms with gate counts that are asymptotically independent of the spectral precision target, reducing resource requirements by several orders of magnitude for a benchmark system.
{"title":"Quantum simulation via stochastic combination of unitaries","authors":"Joseph Peetz, Scott E. Smart, Prineha Narang","doi":"10.1038/s41534-025-01168-w","DOIUrl":"https://doi.org/10.1038/s41534-025-01168-w","url":null,"abstract":"Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit dilations. This naturally enables simulations of open systems, which we demonstrate by preparing damped many-qubit GHZ states on ibm_hanoi. The technique further inspires two Hamiltonian simulation algorithms with gate counts that are asymptotically independent of the spectral precision target, reducing resource requirements by several orders of magnitude for a benchmark system.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"404 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146223205","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}
Pub Date : 2026-02-19DOI: 10.1038/s41534-026-01196-0
Bryce Fuller, Minh C. Tran, Danylo Lykov, Caleb Johnson, Max Rossmannek, Ken Xuan Wei, Andre He, Youngseok Kim, DinhDuy Vu, Kunal Sharma, Yuri Alexeev, Abhinav Kandala, Antonio Mezzacapo
{"title":"Improved quantum computation using operator backpropagation","authors":"Bryce Fuller, Minh C. Tran, Danylo Lykov, Caleb Johnson, Max Rossmannek, Ken Xuan Wei, Andre He, Youngseok Kim, DinhDuy Vu, Kunal Sharma, Yuri Alexeev, Abhinav Kandala, Antonio Mezzacapo","doi":"10.1038/s41534-026-01196-0","DOIUrl":"https://doi.org/10.1038/s41534-026-01196-0","url":null,"abstract":"","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"10 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146223206","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}
Pub Date : 2026-02-16DOI: 10.1038/s41534-026-01186-2
Yovav Tene-Cohen, Tomer Kelman, Ohad Lev, Adi Makmal
MaxCut is a key NP-hard combinatorial optimization problem. Quantum computing offers methods to solve such problems potentially better than classical counterparts, with the Quantum Approximate Optimization Algorithm (QAOA) being a state-of-the-art example. However, the performance of quantum methods is currently hindered by hardware noise and limited qubit volumes. We present a variational Qubit-Efficient MaxCut (QEMC) algorithm that requires only $$O(log N)$$O(logN) qubits to tackle graphs of size N , an exponential reduction compared to QAOA. We demonstrate cutting-edge performance for 32-node graph instances (5 qubits) on real superconducting hardware, and for graphs with up to 2048 nodes (11 qubits) via classical simulations. The QEMC algorithm is based on an innovative encoding scheme, with potentially broad applicability, that empowers it with strong noise resilience, but also enables its efficient classical simulation. As such, the QEMC algorithm provides a challenging benchmark for QAOA on noisy devices and offers a novel quantum-inspired approach.
MaxCut是一个关键的NP-hard组合优化问题。量子计算提供了解决这些问题的方法，可能比经典的方法更好，量子近似优化算法（QAOA）就是一个最先进的例子。然而，量子方法的性能目前受到硬件噪声和有限量子比特体积的阻碍。我们提出了一种变分量子位高效MaxCut （QEMC）算法，它只需要$$O(log N)$$ O （log N）个量子位来处理大小为N的图，与QAOA相比，这是一个指数级的减少。我们在真正的超导硬件上展示了32节点图实例（5个量子比特）的尖端性能，并通过经典模拟展示了多达2048个节点（11个量子比特）的图。QEMC算法基于一种创新的编码方案，具有潜在的广泛适用性，使其具有较强的抗噪声能力，同时也使其能够进行高效的经典模拟。因此，QEMC算法为噪声设备上的QAOA提供了一个具有挑战性的基准，并提供了一种新颖的量子启发方法。
{"title":"A Variational Qubit-Efficient MaxCut Heuristic Algorithm","authors":"Yovav Tene-Cohen, Tomer Kelman, Ohad Lev, Adi Makmal","doi":"10.1038/s41534-026-01186-2","DOIUrl":"https://doi.org/10.1038/s41534-026-01186-2","url":null,"abstract":"MaxCut is a key NP-hard combinatorial optimization problem. Quantum computing offers methods to solve such problems potentially better than classical counterparts, with the Quantum Approximate Optimization Algorithm (QAOA) being a state-of-the-art example. However, the performance of quantum methods is currently hindered by hardware noise and limited qubit volumes. We present a variational Qubit-Efficient MaxCut (QEMC) algorithm that requires only <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$O(log N)$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>log</mml:mi> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> qubits to tackle graphs of size <jats:italic>N</jats:italic> , an exponential reduction compared to QAOA. We demonstrate cutting-edge performance for 32-node graph instances (5 qubits) on real superconducting hardware, and for graphs with up to 2048 nodes (11 qubits) via classical simulations. The QEMC algorithm is based on an innovative encoding scheme, with potentially broad applicability, that empowers it with strong noise resilience, but also enables its efficient classical simulation. As such, the QEMC algorithm provides a challenging benchmark for QAOA on noisy devices and offers a novel quantum-inspired approach.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"52 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146204863","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}
Pub Date : 2026-02-15DOI: 10.1038/s41534-026-01195-1
Min Chen, Jinglei Cheng, Pingzhi Li, Haoran Wang, Tianlong Chen, Junyu Liu
Understanding the high-level conceptual structure of quantum algorithms from their low-level circuit representations is a critical task for verification, debugging, and education. While traditional numerical simulators can calculate output probabilities, they do not explicitly surface the underlying algorithmic logic, such as the function of an oracle or embedded symmetries. In this work, we shift the focus from numerical simulation to symbolic analysis, investigating whether large language models (LLMs) can automatically interpret quantum circuits and articulate their logic in a human-readable format. We introduce GroverGPT+, a model that leverages Chain-of-Thought reasoning and quantum-native tokenization to analyze Grover’s search algorithm. We use Grover’s algorithm as a controlled testbed, as its well-defined analytical properties allow for rigorous verification of the model’s reasoning process. Our primary finding is that GroverGPT+ successfully identifies the oracle and its marked states directly from circuit representations. The model’s key output is not a final probability, but a structured, interpretable reasoning trace that mirrors human expert analysis, effectively translating procedural circuit steps into conceptual insights. Furthermore, we establish a structured benchmark for this symbolic analysis task and explore its empirical extrapolation, describing the model’s performance as the number of qubits increases. These findings position LLMs as powerful tools for automated quantum algorithm analysis and verification. More fundamentally, this work offers a first step towards using such models as scientific probes, suggesting that an algorithm’s “learnability" by a classical model can provide a new, complementary perspective on its conceptual complexity, a topic of core interest to quantum information science.
{"title":"Symbolic analysis of Grover search algorithm via Chain-of-Thought reasoning and quantum-native tokenization","authors":"Min Chen, Jinglei Cheng, Pingzhi Li, Haoran Wang, Tianlong Chen, Junyu Liu","doi":"10.1038/s41534-026-01195-1","DOIUrl":"https://doi.org/10.1038/s41534-026-01195-1","url":null,"abstract":"Understanding the high-level conceptual structure of quantum algorithms from their low-level circuit representations is a critical task for verification, debugging, and education. While traditional numerical simulators can calculate output probabilities, they do not explicitly surface the underlying algorithmic logic, such as the function of an oracle or embedded symmetries. In this work, we shift the focus from numerical simulation to symbolic analysis, investigating whether large language models (LLMs) can automatically interpret quantum circuits and articulate their logic in a human-readable format. We introduce GroverGPT+, a model that leverages Chain-of-Thought reasoning and quantum-native tokenization to analyze Grover’s search algorithm. We use Grover’s algorithm as a controlled testbed, as its well-defined analytical properties allow for rigorous verification of the model’s reasoning process. Our primary finding is that GroverGPT+ successfully identifies the oracle and its marked states directly from circuit representations. The model’s key output is not a final probability, but a structured, interpretable reasoning trace that mirrors human expert analysis, effectively translating procedural circuit steps into conceptual insights. Furthermore, we establish a structured benchmark for this symbolic analysis task and explore its empirical extrapolation, describing the model’s performance as the number of qubits increases. These findings position LLMs as powerful tools for automated quantum algorithm analysis and verification. More fundamentally, this work offers a first step towards using such models as scientific probes, suggesting that an algorithm’s “learnability\" by a classical model can provide a new, complementary perspective on its conceptual complexity, a topic of core interest to quantum information science.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"94 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146196759","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}
Discrete diffusion models typically rely on dimension-wise factorization to avoid computational intractability. However, we rigorously prove this approach leads to worst-case errors scaling linearly with data dimension, fundamentally failing to capture inter-dimensional correlations. To address this, we propose a quantum discrete denoising diffusion probabilistic model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces. By deriving posterior states through quantum Bayes’ theorem, we establish a theoretical foundation for quantum-enhanced diffusion models. We design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Crucially, our approach enables single-step sampling from pure noise to eliminate iterative bottlenecks, while also supporting retraining-free conditional inference, a flexibility often absent in existing quantum generative models such as quantum circuit Born machines. Simulations demonstrate that QD3PM significantly outperforms the parameter-matched classical baseline in modeling inter-dimensional correlations and exhibits superior robustness against quantum noise compared to quantum generative adversarial networks and quantum variational autoencoders. Hence, our work establishes a new theoretical paradigm by leveraging quantum advantages in joint distribution learning.
{"title":"Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning","authors":"Chuangtao Chen, Qinglin Zhao, MengChu Zhou, Dusit Niyato, Zhimin He, Haozhen Situ","doi":"10.1038/s41534-026-01188-0","DOIUrl":"https://doi.org/10.1038/s41534-026-01188-0","url":null,"abstract":"Discrete diffusion models typically rely on dimension-wise factorization to avoid computational intractability. However, we rigorously prove this approach leads to worst-case errors scaling linearly with data dimension, fundamentally failing to capture inter-dimensional correlations. To address this, we propose a quantum discrete denoising diffusion probabilistic model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces. By deriving posterior states through quantum Bayes’ theorem, we establish a theoretical foundation for quantum-enhanced diffusion models. We design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Crucially, our approach enables single-step sampling from pure noise to eliminate iterative bottlenecks, while also supporting retraining-free conditional inference, a flexibility often absent in existing quantum generative models such as quantum circuit Born machines. Simulations demonstrate that QD3PM significantly outperforms the parameter-matched classical baseline in modeling inter-dimensional correlations and exhibits superior robustness against quantum noise compared to quantum generative adversarial networks and quantum variational autoencoders. Hence, our work establishes a new theoretical paradigm by leveraging quantum advantages in joint distribution learning.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"40 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146196760","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}
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