Pub Date : 2025-12-23DOI: 10.1038/s41534-025-01159-x
Hang Zou, Martin Rahm, Anton Frisk Kockum, Simon Olsson
Hybrid quantum-classical algorithms like the variational quantum eigensolver (VQE) show promise for quantum simulations on near-term quantum devices, but are often limited by complex objective functions and expensive optimization procedures. Here, we propose Flow-VQE, a generative framework leveraging conditional normalizing flows with parameterized quantum circuits to efficiently generate high-quality variational parameters. By embedding a generative model into the VQE optimization loop through preference-based training, Flow-VQE enables quantum gradient-free optimization and offers a systematic approach for parameter transfer, accelerating convergence across related problems through warm-started optimization. We compare Flow-VQE to a number of standard benchmarks through numerical simulations on molecular systems, including hydrogen chains, water, ammonia, and benzene. We find that Flow-VQE generally outperforms baseline optimization algorithms, achieving computational accuracy with fewer circuit evaluations (improvements range from modest to more than two orders of magnitude) and, when used to warm-start the optimization of new systems, accelerates subsequent fine-tuning by up to 50-fold compared with Hartree–Fock initialization. Therefore, we believe Flow-VQE can become a pragmatic and versatile paradigm for leveraging generative modeling to reduce the costs of variational quantum algorithms.
{"title":"Generative flow-based warm start of the variational quantum eigensolver","authors":"Hang Zou, Martin Rahm, Anton Frisk Kockum, Simon Olsson","doi":"10.1038/s41534-025-01159-x","DOIUrl":"https://doi.org/10.1038/s41534-025-01159-x","url":null,"abstract":"Hybrid quantum-classical algorithms like the variational quantum eigensolver (VQE) show promise for quantum simulations on near-term quantum devices, but are often limited by complex objective functions and expensive optimization procedures. Here, we propose Flow-VQE, a generative framework leveraging conditional normalizing flows with parameterized quantum circuits to efficiently generate high-quality variational parameters. By embedding a generative model into the VQE optimization loop through preference-based training, Flow-VQE enables quantum gradient-free optimization and offers a systematic approach for parameter transfer, accelerating convergence across related problems through warm-started optimization. We compare Flow-VQE to a number of standard benchmarks through numerical simulations on molecular systems, including hydrogen chains, water, ammonia, and benzene. We find that Flow-VQE generally outperforms baseline optimization algorithms, achieving computational accuracy with fewer circuit evaluations (improvements range from modest to more than two orders of magnitude) and, when used to warm-start the optimization of new systems, accelerates subsequent fine-tuning by up to 50-fold compared with Hartree–Fock initialization. Therefore, we believe Flow-VQE can become a pragmatic and versatile paradigm for leveraging generative modeling to reduce the costs of variational quantum algorithms.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"29 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808180","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 : 2025-12-20DOI: 10.1038/s41534-025-01156-0
Rhea Alexander
Transversal encoded gatesets are highly desirable for fault tolerant quantum computing. However, a quantum error correcting code which exactly corrects for local erasure noise and supports a universal set of transversal gates is ruled out by the Eastin-Knill theorem. Here, we provide a new approximate Eastin-Knill theorem for the single-shot regime when we allow for some probability of error in the decoding. In particular, we show that a quantum error correcting code can support a universal set of transversal gates and approximately correct for local erasure if and only if the conditional min-entropy of the Choi state of the encoding and noise channel is upper bounded by a simple function of the worst-case error probability. Our no-go theorem can be computed by solving a semidefinite program, and, in the spirit of the original Eastin-Knill theorem, is formulated in terms of a condition that is both necessary and sufficient, ensuring achievability whenever it is passed. As an example, we find that with n = 100 physical qutrits we can encode k = 1 logical qubit in the W-state code, which admits a universal transversal set of gates and corrects for single subsystem erasure with error probability of ε = 0.005. To establish our no-go result, we leverage tools from the resource theory of asymmetry, where, in the single-shot regime, a single (output state-dependent) resource monotone governs all state purifications.
{"title":"A new approximate Eastin-Knill theorem","authors":"Rhea Alexander","doi":"10.1038/s41534-025-01156-0","DOIUrl":"https://doi.org/10.1038/s41534-025-01156-0","url":null,"abstract":"Transversal encoded gatesets are highly desirable for fault tolerant quantum computing. However, a quantum error correcting code which exactly corrects for local erasure noise and supports a universal set of transversal gates is ruled out by the Eastin-Knill theorem. Here, we provide a new approximate Eastin-Knill theorem for the single-shot regime when we allow for some probability of error in the decoding. In particular, we show that a quantum error correcting code can support a universal set of transversal gates and approximately correct for local erasure if and only if the conditional min-entropy of the Choi state of the encoding and noise channel is upper bounded by a simple function of the worst-case error probability. Our no-go theorem can be computed by solving a semidefinite program, and, in the spirit of the original Eastin-Knill theorem, is formulated in terms of a condition that is both necessary and sufficient, ensuring achievability whenever it is passed. As an example, we find that with n = 100 physical qutrits we can encode k = 1 logical qubit in the W-state code, which admits a universal transversal set of gates and corrects for single subsystem erasure with error probability of ε = 0.005. To establish our no-go result, we leverage tools from the resource theory of asymmetry, where, in the single-shot regime, a single (output state-dependent) resource monotone governs all state purifications.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"22 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796451","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}
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-π hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.
{"title":"Exceptional-point-induced nonequilibrium entanglement dynamics in bosonic networks","authors":"Chenghe Yu, Mingsheng Tian, Ningxin Kong, Matteo Fadel, Xinyao Huang, Qiongyi He","doi":"10.1038/s41534-025-01158-y","DOIUrl":"https://doi.org/10.1038/s41534-025-01158-y","url":null,"abstract":"Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-π hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"11 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796458","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 : 2025-12-14DOI: 10.1038/s41534-025-01153-3
Zhiyuan Wang, Qing He, Zijing Zhang
Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.
{"title":"Efficient non-destructive direct characterization of arbitrary many-body quantum channels","authors":"Zhiyuan Wang, Qing He, Zijing Zhang","doi":"10.1038/s41534-025-01153-3","DOIUrl":"https://doi.org/10.1038/s41534-025-01153-3","url":null,"abstract":"Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"9 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746785","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 : 2025-12-13DOI: 10.1038/s41534-025-01142-6
Boyuan Wang, Zhaoyuan Meng, Yaomin Zhao, Yue Yang
Quantum computing holds transformative potential for simulating nonlinear physical systems, such as fluid turbulence. However, mapping nonlinear dynamics to the linear operations required by quantum hardware remains a fundamental challenge. Here, we bridge this gap by introducing a novel node-level ensemble description of a lattice gas, which enables the simulation of nonlinear fluid dynamics on quantum computers. This approach combines the advantages of the lattice Boltzmann method with low-dimensional representation (computational cost) and lattice gas cellular automata with linear collision treatment (quantum compatibility). Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality, offering the potential for quantum speedup. We validated the algorithm through simulations of vortex-pair merging and decaying turbulence on up to 16.8 million computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work potentially advances the development of quantum algorithms for other nonlinear problems across various transport phenomena in engineering.
{"title":"Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics","authors":"Boyuan Wang, Zhaoyuan Meng, Yaomin Zhao, Yue Yang","doi":"10.1038/s41534-025-01142-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01142-6","url":null,"abstract":"Quantum computing holds transformative potential for simulating nonlinear physical systems, such as fluid turbulence. However, mapping nonlinear dynamics to the linear operations required by quantum hardware remains a fundamental challenge. Here, we bridge this gap by introducing a novel node-level ensemble description of a lattice gas, which enables the simulation of nonlinear fluid dynamics on quantum computers. This approach combines the advantages of the lattice Boltzmann method with low-dimensional representation (computational cost) and lattice gas cellular automata with linear collision treatment (quantum compatibility). Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality, offering the potential for quantum speedup. We validated the algorithm through simulations of vortex-pair merging and decaying turbulence on up to 16.8 million computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work potentially advances the development of quantum algorithms for other nonlinear problems across various transport phenomena in engineering.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"15 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746830","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 : 2025-12-13DOI: 10.1038/s41534-025-01154-2
Gabriele Agliardi, Giorgio Cortiana, Anton Dekusar, Kumar Ghosh, Naeimeh Mohseni, Corey O’Meara, Víctor Valls, Kavitha Yogaraj, Sergiy Zhuk
Fidelity quantum kernels provide a provable advantage on classification problems where a group structure in the data can be exploited. However, in practical applications, the group structure may be unknown or approximate, and scaling to the ‘utility’ regime is affected by exponential concentration. We prove that an ideal behavior of fidelity kernels is always associated with a (possibly unknown) group structure in the feature map. We also propose a mitigation strategy for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate exponential concentration. Applied to real-world data with unknown structure, related to the charge schedule of electric vehicles, BFT proves useful on 40 + qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through a synthetic dataset with 156 qubits, we obtain an accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum. This constitutes the largest experiment of quantum machine learning on IBM devices to date.
{"title":"Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data","authors":"Gabriele Agliardi, Giorgio Cortiana, Anton Dekusar, Kumar Ghosh, Naeimeh Mohseni, Corey O’Meara, Víctor Valls, Kavitha Yogaraj, Sergiy Zhuk","doi":"10.1038/s41534-025-01154-2","DOIUrl":"https://doi.org/10.1038/s41534-025-01154-2","url":null,"abstract":"Fidelity quantum kernels provide a provable advantage on classification problems where a group structure in the data can be exploited. However, in practical applications, the group structure may be unknown or approximate, and scaling to the ‘utility’ regime is affected by exponential concentration. We prove that an ideal behavior of fidelity kernels is always associated with a (possibly unknown) group structure in the feature map. We also propose a mitigation strategy for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate exponential concentration. Applied to real-world data with unknown structure, related to the charge schedule of electric vehicles, BFT proves useful on 40 + qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through a synthetic dataset with 156 qubits, we obtain an accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum. This constitutes the largest experiment of quantum machine learning on IBM devices to date.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"20 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746787","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 : 2025-12-13DOI: 10.1038/s41534-025-01140-8
Lorenzo Peri, Alberto Gomez-Saiz, Christopher J. B. Ford, M. Fernando Gonzalez-Zalba
Scalable solid-state quantum computers will require integration with analog and digital electronics. Efficiently simulating the quantum-classical electronic interface is hence of paramount importance. Here, we present Verilog-A compact models with a focus on quantum-dot-based systems, relevant to semiconductor- and Majorana-based quantum computing. Our models are capable of faithfully reproducing coherent quantum behavior and decoherence effects within a standard electronic circuit simulator, enabling compromise-free co-simulation of hybrid quantum devices. In particular, we present results from co-simulations performed in Cadence Spectre®, showcasing coherent quantum phenomena in circuits with both quantum and classical components using an industry-standard electronic design and automation tool. Our work paves the way for a new paradigm in the design of quantum systems, which leverages the many decades of development of electronic computer-aided design and automation tools in the semiconductor industry to now simulate and optimize quantum processing units, quantum-classical interfaces, and hybrid quantum-analog circuits.
{"title":"Compact quantum dot models for analog microwave co-simulation","authors":"Lorenzo Peri, Alberto Gomez-Saiz, Christopher J. B. Ford, M. Fernando Gonzalez-Zalba","doi":"10.1038/s41534-025-01140-8","DOIUrl":"https://doi.org/10.1038/s41534-025-01140-8","url":null,"abstract":"Scalable solid-state quantum computers will require integration with analog and digital electronics. Efficiently simulating the quantum-classical electronic interface is hence of paramount importance. Here, we present Verilog-A compact models with a focus on quantum-dot-based systems, relevant to semiconductor- and Majorana-based quantum computing. Our models are capable of faithfully reproducing coherent quantum behavior and decoherence effects within a standard electronic circuit simulator, enabling compromise-free co-simulation of hybrid quantum devices. In particular, we present results from co-simulations performed in Cadence Spectre®, showcasing coherent quantum phenomena in circuits with both quantum and classical components using an industry-standard electronic design and automation tool. Our work paves the way for a new paradigm in the design of quantum systems, which leverages the many decades of development of electronic computer-aided design and automation tools in the semiconductor industry to now simulate and optimize quantum processing units, quantum-classical interfaces, and hybrid quantum-analog circuits.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"7 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746788","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 : 2025-12-12DOI: 10.1038/s41534-025-01155-1
Mengxin Du, Chao Zhang, Yiu Tung Poon, Bei Zeng
Quantum error correction (QEC) is essential for protecting quantum information against noise, yet understanding the structure of the Knill-Laflamme (KL) coefficients (left{{lambda }_{ij}right}) from the condition (P{E}_{i}^{dagger }{E}_{j}P={lambda }_{ij}P) remains challenging, particularly for nonadditive codes. In this work, we introduce the signature vector (overrightarrow{lambda }(P)), composed of the off-diagonal KL coefficients (left{{lambda }_{ij}right}), where each coefficient corresponds to equivalence classes of errors counted only once. We define its Euclidean norm λ*(P) as a scalar measure representing the total strength of error correlations within the code subspace defined by the projector P. We parameterize P on a Stiefel manifold and formulate an optimization problem based on the KL conditions to systematically explore possible values of λ*. Moreover, we show that, for ((n, K, d)) codes, λ* is invariant under local unitary transformations. Applying our approach to the ((6, 2, 3)) quantum code, we find that ({lambda }_{min }^{* }=sqrt{0.6}) and ({lambda }_{max }^{* }=1), with λ* = 1 corresponding to a known degenerate stabilizer code. We construct continuous families of new nonadditive codes parameterized by vectors in ({{mathbb{R}}}^{5}), with λ* varying over the interval ([sqrt{0.6},1]). For the ((7, 2, 3)) code, we identify ({lambda }_{min }^{* }=0) (corresponding to the non-degenerate Steane code) and ({lambda }_{max }^{* }=sqrt{7}) (corresponding to the permutation-invariant code by Pollatsek and Ruskai), and we demonstrate continuous paths connecting these extremes via cyclic codes characterized solely by λ*. Our findings provide new insights into the structure of quantum codes, advance the theoretical foundations of QEC, and open new avenues for investigating intricate relationships between code subspaces and error correlations.
{"title":"Characterizing quantum codes via the coefficients in Knill-Laflamme conditions","authors":"Mengxin Du, Chao Zhang, Yiu Tung Poon, Bei Zeng","doi":"10.1038/s41534-025-01155-1","DOIUrl":"https://doi.org/10.1038/s41534-025-01155-1","url":null,"abstract":"Quantum error correction (QEC) is essential for protecting quantum information against noise, yet understanding the structure of the Knill-Laflamme (KL) coefficients (left{{lambda }_{ij}right}) from the condition (P{E}_{i}^{dagger }{E}_{j}P={lambda }_{ij}P) remains challenging, particularly for nonadditive codes. In this work, we introduce the signature vector (overrightarrow{lambda }(P)), composed of the off-diagonal KL coefficients (left{{lambda }_{ij}right}), where each coefficient corresponds to equivalence classes of errors counted only once. We define its Euclidean norm λ*(P) as a scalar measure representing the total strength of error correlations within the code subspace defined by the projector P. We parameterize P on a Stiefel manifold and formulate an optimization problem based on the KL conditions to systematically explore possible values of λ*. Moreover, we show that, for ((n, K, d)) codes, λ* is invariant under local unitary transformations. Applying our approach to the ((6, 2, 3)) quantum code, we find that ({lambda }_{min }^{* }=sqrt{0.6}) and ({lambda }_{max }^{* }=1), with λ* = 1 corresponding to a known degenerate stabilizer code. We construct continuous families of new nonadditive codes parameterized by vectors in ({{mathbb{R}}}^{5}), with λ* varying over the interval ([sqrt{0.6},1]). For the ((7, 2, 3)) code, we identify ({lambda }_{min }^{* }=0) (corresponding to the non-degenerate Steane code) and ({lambda }_{max }^{* }=sqrt{7}) (corresponding to the permutation-invariant code by Pollatsek and Ruskai), and we demonstrate continuous paths connecting these extremes via cyclic codes characterized solely by λ*. Our findings provide new insights into the structure of quantum codes, advance the theoretical foundations of QEC, and open new avenues for investigating intricate relationships between code subspaces and error correlations.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"112 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746789","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 : 2025-12-09DOI: 10.1038/s41534-025-01150-6
Juan S. Rojas-Arias, Yohei Kojima, Kenta Takeda, Peter Stano, Takashi Nakajima, Jun Yoneda, Akito Noiri, Takashi Kobayashi, Daniel Loss, Seigo Tarucha
We measure and analyze noise-induced energy-fluctuations of spin qubits defined in quantum dots made of isotopically natural silicon. Combining Ramsey, time-correlation of single-shot measurements, and CPMG experiments, we cover the qubit noise power spectrum over a frequency range of nine orders of magnitude without any gaps. We find that the low-frequency noise spectrum is similar across three different devices suggesting that it is dominated by the hyperfine coupling to nuclei. The effects of charge noise are smaller, but not negligible, and are device dependent as confirmed from the noise cross-correlations. We also observe differences to spectra reported in GaAs [Phys. Rev. Lett. 118, 177702 (2017), Phys. Rev. Lett. 101, 236803 (2008)], which we attribute to the presence of the valley degree of freedom in silicon. Finally, we observe ({T}_{2}^{* }) to increase upon increasing the external magnetic field, which we speculate is due to the increasing field gradient of the micromagnet suppressing nuclear spin diffusion.
我们测量和分析了由同位素天然硅制成的量子点中定义的自旋量子比特的噪声诱导能量波动。结合Ramsey、单次测量的时间相关性和CPMG实验，我们在9个数量级的频率范围内覆盖了量子比特噪声功率谱，没有任何间隙。我们发现低频噪声谱在三种不同的器件上是相似的，这表明它是由与原子核的超精细耦合主导的。电荷噪声的影响较小，但不可忽略，并且从噪声相互关系中证实是器件相关的。我们还观察到与GaAs [Phys]中报道的光谱的差异。Rev. Lett. 118,177702 (2017), Phys。Rev. Lett. 101, 236803(2008)]，我们将其归因于硅中谷自由度的存在。最后，我们观察到({T}_{2}^{* })随着外磁场的增大而增大，我们推测这是由于微磁体的场梯度增大抑制了核自旋扩散。
{"title":"The origins of noise in the Zeeman splitting of spin qubits in natural-silicon devices","authors":"Juan S. Rojas-Arias, Yohei Kojima, Kenta Takeda, Peter Stano, Takashi Nakajima, Jun Yoneda, Akito Noiri, Takashi Kobayashi, Daniel Loss, Seigo Tarucha","doi":"10.1038/s41534-025-01150-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01150-6","url":null,"abstract":"We measure and analyze noise-induced energy-fluctuations of spin qubits defined in quantum dots made of isotopically natural silicon. Combining Ramsey, time-correlation of single-shot measurements, and CPMG experiments, we cover the qubit noise power spectrum over a frequency range of nine orders of magnitude without any gaps. We find that the low-frequency noise spectrum is similar across three different devices suggesting that it is dominated by the hyperfine coupling to nuclei. The effects of charge noise are smaller, but not negligible, and are device dependent as confirmed from the noise cross-correlations. We also observe differences to spectra reported in GaAs [Phys. Rev. Lett. 118, 177702 (2017), Phys. Rev. Lett. 101, 236803 (2008)], which we attribute to the presence of the valley degree of freedom in silicon. Finally, we observe ({T}_{2}^{* }) to increase upon increasing the external magnetic field, which we speculate is due to the increasing field gradient of the micromagnet suppressing nuclear spin diffusion.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"27 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705088","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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