For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors that occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of noisy intermediate-scale quantum machines one must seek to mitigate errors rather than completely eliminate them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and describes the hardware demonstrations achieved to date. Commonalities and limitations among the methods are identified, while mention is made of how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified, and the prospects for realizing mitigation-based devices that can deliver a quantum advantage with an impact on science and business are discussed.

Kinematic variables play an important role in collider phenomenology, as they expedite discoveries of new particles by separating signal events from unwanted background events and allow for measurements of particle properties such as masses, couplings, and spins. For the past ten years, an enormous number of kinematic variables have been designed and proposed, primarily for the experiments at the CERN Large Hadron Collider, allowing for a drastic reduction of high-dimensional experimental data to lower-dimensional observables, from which one can readily extract underlying features of phase space and develop better-optimized data-analysis strategies. Recent developments in the area of phase-space kinematics are reviewd, and new kinematic variables with important phenomenological implications and physics applications are summarized. Recently proposed analysis methods and techniques specifically designed to leverage new kinematic variables are also reviewed. As machine learning is currently percolating through many fields of particle physics, including collider phenomenology, the interconnection and mutual complementarity of kinematic variables and machine-learning techniques are discussed. Finally, the manner in which utilization of kinematic variables originally developed for colliders can be extended to other high-energy physics experiments, including neutrino experiments, is discussed.

The optics of correlated disordered media is a conceptually rich research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport, and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This review examines the theoretical foundations, state-of-the-art experimental techniques, and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems: from short-range correlated photonic liquids to Lévy glasses containing fractal heterogeneities to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. Ongoing research on mesoscopic phenomena such as transport phase transitions and speckle statistics and the current development of disorder engineering for applications such as light-energy management and visual appearance design are overviewed. Finally, special efforts are made to identify the main theoretical and experimental challenges to address in the near future.

New particle formation of liquid or solid nanoparticles from gas-phase precursors is a decisive process in Earth’s atmosphere and is considered one of the largest uncertainties in climate change predictions. Key for the climate relevance of new particle formation is the growth of freshly formed molecular clusters, as it determines the survival of these particles to cloud condensation nuclei sizes, where they can contribute to the aerosol-indirect effect. This review lays out the fundamental definitions of nanoparticle growth and addresses the rapidly emerging field of new particle formation studies with a focus on the diverse processes contributing to nanoparticle growth, explicitly comparing the latest experimental findings and their implementation in large-scale models. Atmospheric nanoparticle growth is a complex phenomenon including condensational and reactive vapor uptake, aerosol coagulation, and sink processes. It is linked to thermodynamics, cluster- and phase-transition physics. Nanoparticle growth rates measured from the evolution of the particle-size distribution describe growth as a collective phenomenon, while models often interpret them on a single-particle level and incorporate it into highly simplified size-distribution representations. Recent atmospheric observations show that sulfuric acid together with ammonia and amines, iodic acid, and oxidized organic species can contribute to nanoparticle growth, whereas most models describe the growth effects from a limited subset of this variety of condensable vapors. Atmospheric simulation chamber experiments have clarified the role of ions, intermolecular forces, the interplay of acids and bases, and the contribution of different types of organic vapors. Especially in the complex thermodynamics of organic vapor condensation, the field has had noteworthy advances over the last decade. While the experimental field has achieved significant progress in methodology and process level understanding, this has not led to a similar improvement in the description of the climate impact of nanoparticle formation in large-scale models. This review sets the basis to better align experimental and modeling studies on nanoparticle growth, giving specific guidance for future studies aiming to resolve the questions as to why the climate response in large-scale models seems to be buffered against high survival probabilities and why the global growth observations herein show surprisingly low variation.

Knowing the physicochemical properties of exhaled droplets and aerosol particles is a prerequisite for a detailed mechanistic understanding and effective prevention of the airborne transmission of infectious human diseases. This review provides a critical consideration and synthesis of scientific knowledge on the number concentrations, size distributions, composition, mixing state, and related properties of respiratory particles emitted upon breathing, speaking, singing, coughing, and sneezing. A parametrization of respiratory particle size distributions is derived and presented based on five log-normal modes related to different origins in the respiratory tract, which can be used to trace and localize the sources of infectious particles. This approach may support the medical treatment as well as the risk assessment for aerosol and droplet transmission of infectious diseases. It was applied to analyze which respiratory activities may drive the spread of specific pathogens, such as Mycobacterium tuberculosis, influenza viruses, and severe acute respiratory syndrome coronaviruses 2 (SARS-CoV-2). The results confirm the high relevance of vocalization for the transmission of SARS-CoV-2, as well as the usefulness of physical distancing, face masks, room ventilation, and air filtration as preventative measures against coronavirus disease 2019 and other airborne infectious diseases.

Accelerator mass spectrometry (AMS) was born in the late 1970s, when it was realized at nuclear physics laboratories that the accelerator systems can be used as a sensitive mass spectrometer to measure ultralow traces of long-lived radioisotopes. It soon became possible to measure radioisotope-to-stable-isotope ratios in the range from ${10}^{-12}$ to ${10}^{-16}$ by counting the radioisotope ions “atom by atom” and comparing the count rate with ion currents of stable isotopes ($1.6\mathrm{\mu }\mathrm{A}=1\times {10}^{13}$ singly charged ions/s). It turned out that electrostatic tandem accelerators are best suited for this, and there are now worldwide about 160 AMS facilities based on this principle. This review presents the history, technological developments, and research areas of AMS through the 45 yr since its discovery. Many different fields are touched by AMS measurements, including archaeology, astrophysics, atmospheric science, biology, climatology, cosmic-ray physics, environmental physics, forensic science, glaciology, geophormology, hydrology, ice core research, meteoritics, nuclear physics, oceanography, and particle physics. Since it is virtually impossible to discuss all fields in detail in this review, only specific fields with recent advances are highlighted in detail. For the others, an effort is made to provide relevant references for in-depth studies of the respective fields.

Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Approximately a century ago it was realized that an extension to this type of dynamics can be obtained in the form of “anomalous” diffusion, where distributions are allowed to have heavy power-law tails. Owing to a unique feature of its momentum-dependent dissipative friction force, laser-cooled atomic ensembles can be used as a test bed for such dynamics. The interplay between laser cooling and anomalous dynamics bears deep predictive implications for fundamental concepts in both equilibrium and nonequilibrium statistical physics. The high degree of control available in cold-atom experiments allows for the parameters of the friction to be tuned, revealing transitions in the dynamical properties of the system. Rare events in both the momentum and spatial distributions are described by non-normalized states using tools adapted from infinite ergodic theory. This leads to new experimental and theoretical results that illuminate the various features of the system.

Fast radio bursts (FRBs), millisecond-duration bursts prevailing in the radio sky, are the latest large puzzle in the Universe and have been a subject of intense observational and theoretical investigations in recent years. The rapid accumulation of observational data has painted the following sketch about the physical origin of FRBs: They predominantly originate from cosmological distances, so their sources produce the most extreme coherent radio emission in the Universe; at least some, probably most, FRBs are repeating sources that do not invoke cataclysmic events; and at least some FRBs are produced by magnetars, neutron stars with the strongest magnetic fields in the Universe. Many open questions regarding the physical origin(s) and mechanism(s) of FRBs remain. This review addresses the phenomenology and possible underlying physics of FRBs. Topics include a summary of the observational data, basic plasma physics, general constraints on FRB models from the data, radiation mechanisms, source and environment models, and propagation effects, as well as FRBs as cosmological probes. Current pressing problems and future prospects are also discussed.

The heavy-fermion metal ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ was the first discovered unconventional, non-phonon-mediated superconductor and, for a long time, was believed to exhibit single-band $d$-wave superconductivity, as inferred from various measurements hinting at a nodal gap structure. More recently, however, measurements using a range of techniques at low temperatures ($T⪅0.1\mathrm{K}$) provided evidence for a fully gapped superconducting order parameter. In this Colloquium, after a historical overview the apparently conflicting results of numerous experimental studies on this compound are surveyed. The different theoretical scenarios that have been applied to understanding the particular gap structure are then addressed, including both isotropic (sign-preserving) and anisotropic two-band $s$-wave superconductivity, as well as an effective two-band $d$-wave model, where the latter can explain the currently available experimental data on ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. The lessons from ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ are expected to help uncover the Cooper-pair states in other unconventional, fully gapped superconductors with strongly correlated carriers, and, in particular, highlight the rich variety of such states enabled by orbital degrees of freedom.

This review addresses the method of explicit calculations of interatomic exchange interactions of magnetic materials. This involves exchange mechanisms normally referred to as a Heisenberg exchange, a Dzyaloshinskii-Moriya interaction, and an anisotropic symmetric exchange. The connection between microscopic theories of the electronic structure, such as density functional theory and dynamical mean-field theory, and interatomic exchange is examined. The different aspects of extracting information for an effective spin Hamiltonian that involves thousands of atoms, from electronic structure calculations considering significantly fewer atoms (1–50), is highlighted. Examples of exchange interactions of a large group of materials is presented, which involves heavy elements of the $3d$ period, alloys between transition metals, Heusler compounds, multilayer systems as well as overlayers and adatoms on a substrate, transition metal oxides, $4f$ elements, magnetic materials in two dimensions, and molecular magnets. Where possible, a comparison to experimental data is made that becomes focused on the magnon dispersion. The influence of relativity is reviewed in a few cases, as is the importance of dynamical correlations. Development to theories that handle out-of-equilibrium conditions is also described here. The review ends with a description of extensions of the theories behind explicit calculations of interatomic exchange to nonmagnetic situations, such as those that describe chemical (charge) order and superconductivity.

The weak gravity conjecture holds that in a theory of quantum gravity any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. These related conjectures and the evidence for their validity in the string theory landscape are reviewed. Also reviewed are a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments that claim the conjecture is plausible based on general principles and quantitative arguments for various special cases or analogs of the conjecture. The implications of these conjectures for particle physics, cosmology, general relativity, and mathematics are also outlined. Finally, important directions for future research are highlighted.

In this review recent investigations are summarized of many-body quantum systems with long-range interactions, which are currently realized in Rydberg atom arrays, dipolar systems, trapped-ion setups, and cold atoms in cavities. In these experimental platforms parameters can be easily changed, and control of the range of the interaction has been achieved. The main aim of the review is to present and identify the common and mostly universal features induced by long-range interactions in the behavior of quantum many-body systems. Discussed are the case of strong nonlocal couplings, i.e., the nonadditive regime, and the one in which energy is extensive, but low-energy, long-wavelength properties are altered with respect to the short-range case. When possible, comparisons with the corresponding results for classical systems are presented. Finally, cases of competition with local effects are also reviewed.

This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this concept in the framework of statistical mechanics. Finally, I will briefly mention the cornucopia of applications of these ideas both in physics and in other disciplines.

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently the first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. Here the theoretical underpinning of quantum random sampling is comprehensively reviewed in terms of computational complexity and verifiability, as are the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. Open questions in the field are discussed, and perspectives for the road ahead, including potential applications of quantum random sampling, are provided.

The spontaneous breaking of time-translation symmetry has led to the discovery of a new phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations that result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. The breaking of ergodicity is focused upon as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the ac Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there is a diverse array of strategies to stabilize time-crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time-crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits are reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

Inertial confinement fusion (ICF) has existed as a field of study since the 1970s, but the field was born out of the Cold War. In the decades since the 1960s, pioneering research developing the principles and technologies of ICF has culminated in the creation of three major Department of Energy facilities that still exist today: the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory, the OMEGA laser at the Laboratory for Laser Energetics, and the $Z$ pulsed power facility at Sandia National Laboratories. While the technology of ICF facilities themselves is interesting, this review concentrates upon the physics principles of the targets fielded on U.S. ICF facilities and upon results from the last decade of research. While there have been periods of frustration on the road to ICF ignition, recent research has demonstrated great leaps in understanding what aspects of the implosions need more control. Tangible progress in ICF is evident as burning plasmas and ignited plasmas have recently been generated, repeatedly, on the NIF stemming from decades of science and engineering understanding generated from work at the three previously mentioned facilities and in the international community.

Innovations in fluid mechanics have been leading to better food since ancient history, while creativity in cooking has inspired fundamental breakthroughs in science. This review addresses how recent advances in hydrodynamics are changing food science and the culinary arts and, reciprocally, how the surprising phenomena that arise in the kitchen are leading to new discoveries across the disciplines, including molecular gastronomy, rheology, soft matter, biophysics, medicine, and nanotechnology. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, an introduction and its connections to food are provided, followed by a discussion of how science could be made more accessible and inclusive. The state-of-the-art knowledge is then assessed, the open problems, along with the likely directions for future research and indeed future dishes. New ideas in science and gastronomy are growing rapidly side by side.

The spin degree of freedom of an electron or a nucleus is one of the most basic properties of nature and functions as an excellent qubit, as it provides a natural two-level system that is insensitive to electric fields, leading to long quantum coherence times. This coherence survives when the spin is isolated and controlled within nanometer-scale, lithographically fabricated semiconductor devices, enabling the existing microelectronics industry to help advance spin qubits into a scalable technology. Driven by the burgeoning field of quantum information science, worldwide efforts have developed semiconductor spin qubits to the point where quantum state preparation, multiqubit coherent control, and single-shot quantum measurement are now routine. The small size, high density, long coherence times, and available industrial infrastructure of these qubits provide a highly competitive candidate for scalable solid-state quantum information processing. Here the physics of semiconductor spin qubits is reviewed, with a focus not only on the early achievements of spin initialization, control, and readout in GaAs quantum dots but also on recent advances in Si and Ge spin qubits, including improved charge control and readout, coupling to other quantum degrees of freedom, and scaling to larger system sizes. First introduced are the four major types of spin qubits: single spin qubits, donor spin qubits, singlet triplet spin qubits, and exchange-only spin qubits. The mesoscopic physics of quantum dots, including single-electron charging, valleys, and spin-orbit coupling, are then reviewed. Next a comprehensive overview of the physics of exchange interactions is given, a crucial resource for single- and two-qubit control in spin qubits. The bulk of the review is centered on the presentation of results from each major spin-qubit type, the present limits of fidelity, and an overview of alternative spin-qubit platforms. A physical description of the impact of noise on semiconductor spin qubits, aided in large part by an introduction to the filter-function formalism, is then given. Last, recent efforts to hybridize spin qubits with superconducting systems, including charge-photon coupling, spin-photon coupling, and long-range cavity-mediated spin-spin interactions, are reviewed. Cavity-based readout approaches are also discussed. The review is intended to give an appreciation for the future prospects of semiconductor spin qubits while highlighting the key advances in mesoscopic physics over the past two decades that underlie the operation of modern quantum-dot and donor spin qubits.

The discovery of neutrinoless $\beta \beta$ decay could soon be within reach. This hypothetical ultrarare nuclear decay offers a privileged portal to physics beyond the standard model of particle physics. Its observation would constitute the discovery of a matter-creating process, corroborating leading theories of why the Universe contains more matter than antimatter, and how forces unify at high energy scales. It would also prove that neutrinos and antineutrinos are not two distinct particles but can transform into each other, with their mass described by a unique mechanism conceived by Majorana. The recognition that neutrinos are not massless necessitates an explanation and has boosted interest in neutrinoless $\beta \beta$ decay. The field stands now at a turning point. A new round of experiments is currently being prepared for the next decade to cover an important region of parameter space. In parallel, advances in nuclear theory are laying the groundwork to connect the nuclear decay with the underlying new physics. Meanwhile, the particle theory landscape continues to find new motivations for neutrinos to be their own antiparticle. This review brings together the experimental, nuclear theory, and particle theory aspects connected to neutrinoless $\beta \beta$ decay to explore the path toward, and beyond, its discovery.