Mathematics and computing articles within Nature Physics

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  • Article
    | Open Access

    Previous work on the limits of quantum information processing has often assumed access to unlimited computational resources. Imposing a requirement for computational efficiency on entanglement theory substantially changes what is possible.

    • Lorenzo Leone
    • , Jacopo Rizzo
    •  & Sofiene Jerbi

  • Comment |

    In this comment, we consider how artificial intelligence tools are reshaping the way mathematical research is conducted and discuss how future developments of this technology will transform mathematical practice.

    • Bartosz Naskręcki
    •  & Ken Ono

  • Article |

    The creation and purification of magic states can be a limiting step in quantum computing. Now an error correcting code has been found where the overhead of this process is the lowest value possible, showing that optimal performance can be achieved.

    • Adam Wills
    • , Min-Hsiu Hsieh
    •  & Hayata Yamasaki

  • Measure for Measure |

    Knowledge gained by combining measurements and simulations leads to increased confidence in the safety of products, as Louise Wright explains.

    • Louise Wright

  • Measure for Measure |

    From monitoring sea-level changes at the millimetre-level to navigating through the streets of Gothenburg, Karine Le Bail discusses the need for precise positioning within well-defined 3D terrestrial and celestial reference frames.

    • Karine Le Bail

  • Article
    | Open Access

    The connection between classical neural networks and Gaussian processes is a fundamental result in machine learning. It has now been shown that many quantum neural networks converge to Gaussian processes, enabling their use for regression tasks.

    • Diego García-Martín
    • , Martín Larocca
    •  & M. Cerezo

  • Perspective |

    Higher-order interactions reveal new aspects of the interplay between topology and dynamics in complex systems. This Perspective describes the emerging field of higher-order topological dynamics and discusses the open research questions in the area.

    • Ana P. Millán
    • , Hanlin Sun
    •  & Ginestra Bianconi

  • Article |

    In general, it is difficult to identify the global energy minimum of a many-body system. Now, it has been shown that finding even local minima is difficult classically but efficiently achievable with a quantum computer.

    • Chi-Fang Chen
    • , Hsin-Yuan Huang
    •  & Leo Zhou

  • News & Views |

    Energetic ions in nuclear fusion devices influence the behaviour of modes at the plasma edge, potentially increasing the risk for particle losses and damage to the device. This introduces additional challenges for the development of fusion reactors.

    • Chang Liu
    •  & Qiming Hu

  • Measure for Measure |

    The Fisher information imposes a fundamental limit on the precision with which an unknown parameter can be estimated from noisy data, as Dorian Bouchet explains.

    • Dorian Bouchet

  • News & Views |

    Recent experimental claims of quantum advantage rely on the absence of classical algorithms that can reproduce the results. A tensor network algorithm can now challenge recent optical quantum advantage experiments.

    • Jordi Tura

  • Research Briefing |

    An improved optimization algorithm enables the training of large-scale neural quantum states in which the enormous number of neuron connections capture the intricate complexity of quantum many-body wavefunctions. This advance leads to unprecedented accuracy in paradigmatic quantum models, opening up new avenues for simulating and understanding complex quantum phenomena.

  • Article
    | Open Access

    The complexity of a many-body quantum state grows exponentially with system size, hindering numerical studies. A unitary flow-based method now enables accurate estimates of long-term properties of one- and two-dimensional quantum systems.

    • S. J. Thomson
    •  & J. Eisert

  • Article
    | Open Access

    An optimization algorithm reduces the cost of training large-scale neural quantum states. This leads to accurate computations of the ground states of frustrated magnets and provides evidence of gapless quantum-spin-liquid phases.

    • Ao Chen
    •  & Markus Heyl

  • Article |

    Timeliness is a crucial property for the optimal functioning of socio-technical systems where delays can propagate. Now it is shown that a stylized model of delay propagation on temporal networks shows a phase transition that can trigger avalanches.

    • José Moran
    • , Matthijs Romeijnders
    •  & Jean-Philippe Bouchaud

  • News & Views |

    Spatial heterogeneity in disease transmission rates and in mixing patterns between regions makes predicting epidemic trajectories hard. Quantifying the mixing rates within and between spatial regions can improve predictions.

    • Emily Paige Harvey
    •  & Dion R. J. O’Neale

  • Article |

    Many recent experiments have stored quantum information in bosonic modes, such as photons in resonators or optical fibres. Now an adaptation of the classical spherical codes provides a framework for designing quantum error correcting codes for these platforms.

    • Shubham P. Jain
    • , Joseph T. Iosue
    •  & Victor V. Albert

  • News & Views |

    The Hamiltonian describing a quantum many-body system can be learned using measurements in thermal equilibrium. Now, a learning algorithm applicable to many natural systems has been found that requires exponentially fewer measurements than existing methods.

    • Sitan Chen

  • Article |

    Cytoplasmic flows in the fruit fly oocyte can reorganize cellular components. These structured vortical flows arise through self-organizing dynamics of microtubules, molecular motors and cytoplasm.

    • Sayantan Dutta
    • , Reza Farhadifar
    •  & Michael J. Shelley

  • Article
    | Open Access

    The transition from a metastable state to the ground state in classical many-body systems is mediated by bubble nucleation. This transition has now been experimentally observed in a quantum setting using coupled atomic superfluids.

    • A. Zenesini
    • , A. Berti
    •  & G. Ferrari

  • News & Views |

    Predicting the large-scale behaviour of complex systems is challenging because of their underlying nonlinear dynamics. Theoretical evidence now verifies that many complex systems can be simplified and still provide an insightful description of the phenomena of interest.

    • Jianxi Gao

  • Article |

    Although using low-rank matrices is the go-to approach to model the dynamics of complex systems, its validity remains formally unconfirmed. An analysis of random networks and real-world data now sheds light on this low-rank hypothesis and its implications.

    • Vincent Thibeault
    • , Antoine Allard
    •  & Patrick Desrosiers

  • Article |

    It has been suggested that Gaussian boson sampling may provide a quantum computational advantage for calculating the vibronic spectra of molecules. Now, an equally efficient classical algorithm has been identified.

    • Changhun Oh
    • , Youngrong Lim
    •  & Liang Jiang

  • News & Views |

    Physical networks, composed of nodes and links that occupy a spatial volume, are hard to study with conventional techniques. A meta-graph approach that elucidates the impact of physicality on network structure has now been introduced.

    • Zoltán Toroczkai

  • Article |

    Physical networks are systems composed of physical entities, which conventional graph-based approaches fail to capture. Theoretical work now introduces a meta-graph technique to uncover the impact of physicality on the structure of networks.

    • Márton Pósfai
    • , Balázs Szegedy
    •  & Albert-László Barabási

  • Article |

    Network geometry is an emerging framework used to describe several topological and organizational features of complex networks. Now this approach has been extended to directed networks, which contain both symmetric and asymmetric interactions.

    • Antoine Allard
    • , M. Ángeles Serrano
    •  & Marián Boguñá

  • Article |

    Being able to perform qubit measurements within a quantum circuit and adapt to their outcome broadens the power of quantum computers. These mid-circuit measurements have now been used to implement a cryptographic proof of non-classical behaviour.

    • Daiwei Zhu
    • , Gregory D. Kahanamoku-Meyer
    •  & Christopher Monroe

  • Article |

    Quantum computers are believed to exponentially outperform classical computers at some tasks, but it is hard to make guarantees about the limits of classical computers. It has now been proven that classical computers cannot efficiently simulate most quantum circuits.

    • Ramis Movassagh

  • Article
    | Open Access

    Elastoviscoplastic fluids combine solid- and liquid-like behaviour depending on applied stress. Simulations of elastoviscoplastic fluids at high Reynolds number now show that plasticity plays a key role in the turbulent flows seen in these systems, leading for example to intermittency.

    • Mohamed S. Abdelgawad
    • , Ianto Cannon
    •  & Marco E. Rosti

  • Article |

    Quantum operations can be considered as points in a high-dimensional space in which distance reflects the similarity of two operations. Applying differential-geometric methods in this picture gives insights into the complexity of quantum systems.

    • Adam R. Brown

  • Comment |

    An analysis of representations of fluid flows in classical paintings reveals scientific inaccuracies. Some of these misrepresentations might be caused by a limited understanding of fluid dynamics and others by deliberate artistic choices.

    • Rouslan Krechetnikov

  • News & Views |

    Experiments with small flocks of sheep show intermittent collective motion events driven by random leaders that guide the group. A model reveals information pooling capabilities, suggesting a mechanism for swarm intelligence.

    • Cristián Huepe

  • Research Briefing |

    The formation of bubbles at liquid–liquid interfaces is challenging to explain because gas pockets cannot be stabilized by cracks on solid impurities. Experiments show that a difference in the gas solubilities of two immiscible liquids provides a gas reservoir, which allows gas to accumulate at the interface, leading to bubble formation.

  • Comment |

    Fluid simulations today are remarkably realistic. In this Comment I discuss some of the most striking results from the past 20 years of computer graphics research that made this happen.

    • Károly Zsolnai-Fehér

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