Pub Date : 2025-12-10DOI: 10.1038/s41567-025-03127-w
Karen Mudryk
Despite being derived from the unit of time, the hertz is a unit in its own right. It has remained a much beloved unit since its establishment almost one hundred years ago, as Karen Mudryk recounts.
{"title":"Love hertz","authors":"Karen Mudryk","doi":"10.1038/s41567-025-03127-w","DOIUrl":"10.1038/s41567-025-03127-w","url":null,"abstract":"Despite being derived from the unit of time, the hertz is a unit in its own right. It has remained a much beloved unit since its establishment almost one hundred years ago, as Karen Mudryk recounts.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"21 12","pages":"2009-2009"},"PeriodicalIF":18.4,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145719858","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 : 2025-12-08DOI: 10.1038/s41567-025-03094-2
Tatsuhiro Onodera, Martin M. Stein, Benjamin A. Ash, Mandar M. Sohoni, Melissa Bosch, Ryotatsu Yanagimoto, Marc Jankowski, Timothy P. McKenna, Tianyu Wang, Gennady Shvets, Maxim R. Shcherbakov, Logan G. Wright, Peter L. McMahon
Controlled multimode wave propagation can enable more space-efficient photonic processors than architectures based on discrete components connected by single-mode waveguides. Instead of defining discrete elements, one can sculpt the continuous substrate of a photonic processor to perform computations through multimode interference in two dimensions. Here we designed and demonstrated a device with a refractive index that can be rapidly reprogrammed across space, allowing arbitrary control of wave propagation. The device, a two-dimensional programmable waveguide, uses parallel electro-optic modulation of the refractive index of a slab waveguide with about 104 programmable spatial degrees of freedom. We implemented neural network inference on benchmark tasks with up to 49-dimensional vectors in a single pass, without digital pre-processing or post-processing. Theoretical and numerical analyses further indicated that two-dimensional programmable waveguides may offer not only a constant-factor reduction in device area but also a scaling benefit, with the area required growing as N1.5 rather than N2. Photonic processors are limited by the bulkiness of discrete components and wiring complexity. An experiment now demonstrates a reprogrammable two-dimensional waveguide that performs neural network inference through multimode wave propagation.
{"title":"Arbitrary control over multimode wave propagation for machine learning","authors":"Tatsuhiro Onodera, Martin M. Stein, Benjamin A. Ash, Mandar M. Sohoni, Melissa Bosch, Ryotatsu Yanagimoto, Marc Jankowski, Timothy P. McKenna, Tianyu Wang, Gennady Shvets, Maxim R. Shcherbakov, Logan G. Wright, Peter L. McMahon","doi":"10.1038/s41567-025-03094-2","DOIUrl":"10.1038/s41567-025-03094-2","url":null,"abstract":"Controlled multimode wave propagation can enable more space-efficient photonic processors than architectures based on discrete components connected by single-mode waveguides. Instead of defining discrete elements, one can sculpt the continuous substrate of a photonic processor to perform computations through multimode interference in two dimensions. Here we designed and demonstrated a device with a refractive index that can be rapidly reprogrammed across space, allowing arbitrary control of wave propagation. The device, a two-dimensional programmable waveguide, uses parallel electro-optic modulation of the refractive index of a slab waveguide with about 104 programmable spatial degrees of freedom. We implemented neural network inference on benchmark tasks with up to 49-dimensional vectors in a single pass, without digital pre-processing or post-processing. Theoretical and numerical analyses further indicated that two-dimensional programmable waveguides may offer not only a constant-factor reduction in device area but also a scaling benefit, with the area required growing as N1.5 rather than N2. Photonic processors are limited by the bulkiness of discrete components and wiring complexity. An experiment now demonstrates a reprogrammable two-dimensional waveguide that performs neural network inference through multimode wave propagation.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"164-171"},"PeriodicalIF":18.4,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s41567-025-03094-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145711516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-05DOI: 10.1038/s41567-025-03126-x
Xiaomeng Liu, Zhida Liu
A fractal energy pattern known as the Hofstadter butterfly has now been observed separately for each spin in a two-dimensional semiconductor, revealing a cascade of magnetic transitions.
{"title":"Hofstadter’s butterfly turns magnetic","authors":"Xiaomeng Liu, Zhida Liu","doi":"10.1038/s41567-025-03126-x","DOIUrl":"10.1038/s41567-025-03126-x","url":null,"abstract":"A fractal energy pattern known as the Hofstadter butterfly has now been observed separately for each spin in a two-dimensional semiconductor, revealing a cascade of magnetic transitions.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"21 12","pages":"1873-1874"},"PeriodicalIF":18.4,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680176","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 : 2025-12-04DOI: 10.1038/s41567-025-03115-0
Jie Liang, Hao Zheng, Feng Jin, Ruiqi Bao, Kevin Dini, Jiahao Ren, Yuxi Liu, Mateusz Król, Elena A. Ostrovskaya, Eliezer Estrecho, Baile Zhang, Timothy C. H. Liew, Rui Su
Non-Hermitian physics has recently transformed our understanding of topology by uncovering a range of effects that are unique to systems with gain and loss. The realization of non-Hermitian topology in strongly coupled light–matter systems not only offers degrees of freedom for the enhanced manipulation of topological phenomena, but is also promising for developing on-chip active photonic devices. Exciton–polaritons—strongly coupled quasiparticles from excitons and photons—emerge as a promising candidate with intrinsic non-Hermitian features. However, limited by the challenges in achieving non-reciprocity, the experimental observation of non-Hermitian topology and its associated transport features has remained elusive. Here we experimentally demonstrate the non-Hermitian topology of exciton–polaritons induced by a twist degree of freedom in a liquid-crystal-filled CsPbBr3 perovskite microcavity at room temperature. The geometric twist between birefringent perovskites and liquid crystals acts as a degree of freedom to tailor the polaritonic complex spectra, leading to non-Hermitian bands with spectral winding topology and non-reciprocity. Furthermore, the induced non-Hermitian topology gives rise to the non-Hermitian exciton–polariton skin effect in real space, manifesting as polariton accumulation at open boundaries. Our findings open new perspectives on tunable non-Hermitian phenomena and the development of on-chip polaritonic devices with enhanced functionalities. Strongly coupled light–matter systems could offer enhanced manipulation of topological phenomena. Now, tunable non-Hermitian effects are demonstrated with exciton–polaritons induced by a twist degree of freedom.
{"title":"Twist-induced non-Hermitian topology of exciton–polaritons","authors":"Jie Liang, Hao Zheng, Feng Jin, Ruiqi Bao, Kevin Dini, Jiahao Ren, Yuxi Liu, Mateusz Król, Elena A. Ostrovskaya, Eliezer Estrecho, Baile Zhang, Timothy C. H. Liew, Rui Su","doi":"10.1038/s41567-025-03115-0","DOIUrl":"10.1038/s41567-025-03115-0","url":null,"abstract":"Non-Hermitian physics has recently transformed our understanding of topology by uncovering a range of effects that are unique to systems with gain and loss. The realization of non-Hermitian topology in strongly coupled light–matter systems not only offers degrees of freedom for the enhanced manipulation of topological phenomena, but is also promising for developing on-chip active photonic devices. Exciton–polaritons—strongly coupled quasiparticles from excitons and photons—emerge as a promising candidate with intrinsic non-Hermitian features. However, limited by the challenges in achieving non-reciprocity, the experimental observation of non-Hermitian topology and its associated transport features has remained elusive. Here we experimentally demonstrate the non-Hermitian topology of exciton–polaritons induced by a twist degree of freedom in a liquid-crystal-filled CsPbBr3 perovskite microcavity at room temperature. The geometric twist between birefringent perovskites and liquid crystals acts as a degree of freedom to tailor the polaritonic complex spectra, leading to non-Hermitian bands with spectral winding topology and non-reciprocity. Furthermore, the induced non-Hermitian topology gives rise to the non-Hermitian exciton–polariton skin effect in real space, manifesting as polariton accumulation at open boundaries. Our findings open new perspectives on tunable non-Hermitian phenomena and the development of on-chip polaritonic devices with enhanced functionalities. Strongly coupled light–matter systems could offer enhanced manipulation of topological phenomena. Now, tunable non-Hermitian effects are demonstrated with exciton–polaritons induced by a twist degree of freedom.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"151-157"},"PeriodicalIF":18.4,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664780","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 : 2025-12-03DOI: 10.1038/s41567-025-03116-z
Shai Tsesses, Aviv Karnieli
Controlling topological photonic quasiparticles is a prerequisite for their implementation in devices. Now, their precise manipulation has been demonstrated using synthetic gauge fields based on the manipulation of the material’s dielectric index.
{"title":"Electrically tuned light topology","authors":"Shai Tsesses, Aviv Karnieli","doi":"10.1038/s41567-025-03116-z","DOIUrl":"10.1038/s41567-025-03116-z","url":null,"abstract":"Controlling topological photonic quasiparticles is a prerequisite for their implementation in devices. Now, their precise manipulation has been demonstrated using synthetic gauge fields based on the manipulation of the material’s dielectric index.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"21 12","pages":"1869-1870"},"PeriodicalIF":18.4,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664606","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 : 2025-12-02DOI: 10.1038/s41567-025-03101-6
Henrik Weyer, Tobias A. Roth, Erwin Frey
For cellular functions such as division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and parameters to the pattern type and dynamics in these protein systems. Here we discover a generic mechanism giving rise to an effective interfacial tension organizing the macroscopic structure of non-equilibrium steady-state patterns. Namely, maintaining protein-density interfaces by cyclic protein attachment and detachment produces curvature-dependent protein redistribution, which straightens the interface. We develop a non-equilibrium Neumann angle law and Plateau vertex conditions for interface junctions and mesh patterns, thus introducing the concepts of ‘Turing mixtures’ and ‘Turing foams’. In contrast to liquid foams and mixtures, these non-equilibrium patterns can select an intrinsic wavelength by interrupting an equilibrium-like coarsening process. Data from in vitro experiments with the Escherichia coli Min protein system verify the vertex conditions and support the wavelength dynamics. Our study shows how interface laws with correspondence to thermodynamic relations can arise from distinct physical processes in active systems. It allows the design of specific pattern morphologies with potential applications as spatial control strategies in synthetic cells. Protein patterns enable cellular processes. A general theory now identifies a non-equilibrium mechanism that generates an effective interfacial tension, shaping the geometry and intrinsic length scales of steady-state protein patterns.
{"title":"Protein pattern morphology and dynamics emerging from effective interfacial tension","authors":"Henrik Weyer, Tobias A. Roth, Erwin Frey","doi":"10.1038/s41567-025-03101-6","DOIUrl":"10.1038/s41567-025-03101-6","url":null,"abstract":"For cellular functions such as division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and parameters to the pattern type and dynamics in these protein systems. Here we discover a generic mechanism giving rise to an effective interfacial tension organizing the macroscopic structure of non-equilibrium steady-state patterns. Namely, maintaining protein-density interfaces by cyclic protein attachment and detachment produces curvature-dependent protein redistribution, which straightens the interface. We develop a non-equilibrium Neumann angle law and Plateau vertex conditions for interface junctions and mesh patterns, thus introducing the concepts of ‘Turing mixtures’ and ‘Turing foams’. In contrast to liquid foams and mixtures, these non-equilibrium patterns can select an intrinsic wavelength by interrupting an equilibrium-like coarsening process. Data from in vitro experiments with the Escherichia coli Min protein system verify the vertex conditions and support the wavelength dynamics. Our study shows how interface laws with correspondence to thermodynamic relations can arise from distinct physical processes in active systems. It allows the design of specific pattern morphologies with potential applications as spatial control strategies in synthetic cells. Protein patterns enable cellular processes. A general theory now identifies a non-equilibrium mechanism that generates an effective interfacial tension, shaping the geometry and intrinsic length scales of steady-state protein patterns.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"94-102"},"PeriodicalIF":18.4,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s41567-025-03101-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1038/s41567-025-03098-y
Heng Wang, Yuying Zhu, Zhonghua Bai, Zhaozheng Lyu, Jiangang Yang, Lin Zhao, X. J. Zhou, Qi-Kun Xue, Ding Zhang
The superconducting diode is a device that allows supercurrent to flow in one direction but not the other. Usually, the state that does not allow supercurrent has no Cooper pairs. Here we report a quantized version of the superconducting diode that operates solely between Cooper-paired states. This type of quantum superconducting diode takes advantage of quantized Shapiro steps for digitized output. The device consists of twisted high-temperature cuprate superconductors and exhibits the following characteristics. First, we show that a non-reciprocal diode behaviour can be initiated by training with current pulses without applying an external magnetic field. Then, we demonstrate perfect diode efficiency under microwave irradiation above liquid-nitrogen temperature. Lastly, the quantized nature of the output offers high resilience against input noise. These features open up opportunities to develop practical dissipationless quantum circuits. A device for rectifying supercurrents at liquid-nitrogen temperature with high efficiency is demonstrated. This is a practical step towards implementing dissipationless electronics.
{"title":"Quantum superconducting diode effect with perfect efficiency above liquid-nitrogen temperature","authors":"Heng Wang, Yuying Zhu, Zhonghua Bai, Zhaozheng Lyu, Jiangang Yang, Lin Zhao, X. J. Zhou, Qi-Kun Xue, Ding Zhang","doi":"10.1038/s41567-025-03098-y","DOIUrl":"10.1038/s41567-025-03098-y","url":null,"abstract":"The superconducting diode is a device that allows supercurrent to flow in one direction but not the other. Usually, the state that does not allow supercurrent has no Cooper pairs. Here we report a quantized version of the superconducting diode that operates solely between Cooper-paired states. This type of quantum superconducting diode takes advantage of quantized Shapiro steps for digitized output. The device consists of twisted high-temperature cuprate superconductors and exhibits the following characteristics. First, we show that a non-reciprocal diode behaviour can be initiated by training with current pulses without applying an external magnetic field. Then, we demonstrate perfect diode efficiency under microwave irradiation above liquid-nitrogen temperature. Lastly, the quantized nature of the output offers high resilience against input noise. These features open up opportunities to develop practical dissipationless quantum circuits. A device for rectifying supercurrents at liquid-nitrogen temperature with high efficiency is demonstrated. This is a practical step towards implementing dissipationless electronics.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"47-53"},"PeriodicalIF":18.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611513","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 : 2025-11-28DOI: 10.1038/s41567-025-03104-3
Adding momentum mixing in a controllable way to the exactly solvable Hatsugai–Kohmoto model is shown to recover the physics of the Hubbard model, the starting point for understanding Mott physics. The scheme converges as the inverse square of the number of steps, and, as each step is tractable, minimal computational resources are required.
{"title":"Momentum mixing solves the Mott problem","authors":"","doi":"10.1038/s41567-025-03104-3","DOIUrl":"10.1038/s41567-025-03104-3","url":null,"abstract":"Adding momentum mixing in a controllable way to the exactly solvable Hatsugai–Kohmoto model is shown to recover the physics of the Hubbard model, the starting point for understanding Mott physics. The scheme converges as the inverse square of the number of steps, and, as each step is tractable, minimal computational resources are required.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"17-18"},"PeriodicalIF":18.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611518","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 : 2025-11-27DOI: 10.1038/s41567-025-03095-1
Peizhi Mai, Jinchao Zhao, Gaurav Tenkila, Nico A. Hackner, Dhruv Kush, Derek Pan, Philip W. Phillips
The Hubbard model is a standard theoretical tool for studying materials with strong electron–electron interactions, such as cuprate superconductors. Unfortunately, interaction-driven phenomena, such as a transition into the strongly correlated Mott insulator phase, are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai–Kohmoto model displays similar Mott physics. Here we show how the Hatsugai–Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically reintroduce all the momentum mixing that the original Hatsugai–Kohmoto model omits. This can be accomplished by grouping n momenta into a cell and hybridizing them, resulting in the momentum-mixing Hatsugai–Kohmoto model. We recover the Bethe ansatz ground-state energy of the one-dimensional Hubbard model to within 1% from only ten mixed momenta. Overall, the convergence scales as 1/n2 as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all the known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe that the momentum-mixing Hatsugai–Kohmoto model offers an alternative tool for strongly correlated quantum matter. The Hubbard model describes the physics of strongly correlated electron systems, but is difficult to solve. Now, a scheme to systematically and efficiently relate the exactly solvable Hatsugai–Kohmoto model to the Hubbard model has been identified.
{"title":"Twisting the Hubbard model into the momentum-mixing Hatsugai–Kohmoto model","authors":"Peizhi Mai, Jinchao Zhao, Gaurav Tenkila, Nico A. Hackner, Dhruv Kush, Derek Pan, Philip W. Phillips","doi":"10.1038/s41567-025-03095-1","DOIUrl":"10.1038/s41567-025-03095-1","url":null,"abstract":"The Hubbard model is a standard theoretical tool for studying materials with strong electron–electron interactions, such as cuprate superconductors. Unfortunately, interaction-driven phenomena, such as a transition into the strongly correlated Mott insulator phase, are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai–Kohmoto model displays similar Mott physics. Here we show how the Hatsugai–Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically reintroduce all the momentum mixing that the original Hatsugai–Kohmoto model omits. This can be accomplished by grouping n momenta into a cell and hybridizing them, resulting in the momentum-mixing Hatsugai–Kohmoto model. We recover the Bethe ansatz ground-state energy of the one-dimensional Hubbard model to within 1% from only ten mixed momenta. Overall, the convergence scales as 1/n2 as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all the known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe that the momentum-mixing Hatsugai–Kohmoto model offers an alternative tool for strongly correlated quantum matter. The Hubbard model describes the physics of strongly correlated electron systems, but is difficult to solve. Now, a scheme to systematically and efficiently relate the exactly solvable Hatsugai–Kohmoto model to the Hubbard model has been identified.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"81-87"},"PeriodicalIF":18.4,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145608805","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 : 2025-11-26DOI: 10.1038/s41567-025-03102-5
Shiro Tamiya, Masato Koashi, Hayata Yamasaki
A major challenge in fault-tolerant quantum computation is to reduce both the space overhead, that is, the large number of physical qubits per logical qubit, and the time overhead, that is, the long physical gate sequences needed to implement a logical gate. Here we prove that a protocol using non-vanishing-rate quantum low-density parity-check (QLDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for the required classical processing. This protocol offers an improvement over existing constant-space-overhead protocols. To prove our result, we develop a technique that we call partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets. With this approach, we resolve a logical gap in the existing arguments for the threshold theorem for the constant-space-overhead protocol with QLDPC codes and complete its proof. Our work establishes that the QLDPC-code-based approach can realize fault-tolerant quantum computation with a negligibly small slowdown and a bounded overhead of physical qubits. Quantum low-density parity-check codes are anticipated to be an efficient approach to quantum error correction. Now it has been proven that these codes can be time-efficient with only a constant overhead in the required number of qubits.
{"title":"Fault-tolerant quantum computation with polylogarithmic time and constant space overheads","authors":"Shiro Tamiya, Masato Koashi, Hayata Yamasaki","doi":"10.1038/s41567-025-03102-5","DOIUrl":"10.1038/s41567-025-03102-5","url":null,"abstract":"A major challenge in fault-tolerant quantum computation is to reduce both the space overhead, that is, the large number of physical qubits per logical qubit, and the time overhead, that is, the long physical gate sequences needed to implement a logical gate. Here we prove that a protocol using non-vanishing-rate quantum low-density parity-check (QLDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for the required classical processing. This protocol offers an improvement over existing constant-space-overhead protocols. To prove our result, we develop a technique that we call partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets. With this approach, we resolve a logical gap in the existing arguments for the threshold theorem for the constant-space-overhead protocol with QLDPC codes and complete its proof. Our work establishes that the QLDPC-code-based approach can realize fault-tolerant quantum computation with a negligibly small slowdown and a bounded overhead of physical qubits. Quantum low-density parity-check codes are anticipated to be an efficient approach to quantum error correction. Now it has been proven that these codes can be time-efficient with only a constant overhead in the required number of qubits.","PeriodicalId":19100,"journal":{"name":"Nature Physics","volume":"22 1","pages":"27-32"},"PeriodicalIF":18.4,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s41567-025-03102-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145599385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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